IODS course project
About the project
At first overwhelming for non experienced programmers or advanced users in the computer field. Nonetheless, after a few hours of careful reading instructions and many self learning sessions in the provided tools one can start to understand that sky is the limit for the stubborn and motivated individuals.
This course will allow you to master R language and give you insights in the possible ways you can use it to analyse different kinds of data.
My Repository: https://github.com/ElsaMarques/IODS-project.git
My learning diary: https://elsamarques.github.io/IODS-project/
1 Tools and methods for open and reproducible research
This chapter allows you to learn how to use the course Softwares (RStudio & GitHub desktop & GitHub) and get the first contact with some of the basic RMarkdown codes
1.1 Work done during the week and learning summary.
- Completed the following courses on DataCamp:
“R short and sweet” ;
“Introduction to R” (Extra ; highly recommend the daily exercises after finishing up this course, perfect and quick way to remind little things you learn till this moment);
“DataCamp (EXTRA): Helsinki Social Statistics” (Similar to the mandatory “R short and Sweet” but nothing like practicing to solidify the learn code, fucntions, etc.. )
1st free chapters of “Intermediate R”" ; “Cleaning Data in R” & “Data manipulation in R With dplyr” (Extra ; gave a clear idea on how complex this can become and once again good practice/reminder of basics learnt till now)
Installed RStudio, GitHub desktop, and explored the RMarkdown Basics & R Code Chunks provided help lists.
Edited my profile picture and explored GitHub settings (Extra)
Succesfully forked the IODS project to personal repository & found my own repository and course diary link
Created the new file RMarkdown (README.Rmd)
Altered the team of the course diary in online GitHub (Extra)
Commited to my branch of the master repostiory my intermediate and final changes
Started working in the chapter2.Rmd by accident but sucessfully hide it from the 1st peer-review deadline
Managed to fix an error message in RStudio start up (Mac OS El Capitan version incompatibility)
2 Regression and model validation
During this chapter the amount of information to be memorized is higher and more complex. The datacamp exercise, including the videos included in it touch the surface of what you can do to build graphs to visualize and analyse your data. Note that during this chapter you will definetily need to consult external help cheats (mostly provided during the datacamp and your mooc links)
2.1 1. Data wrangling exercise
Load the data set provided (questionary answers regarding learning approaches and students accomplishments in a statistics course):
- All data provided in the url
#read the data from URL provided link
lrn14 <- read.table("http://www.helsinki.fi/~kvehkala/JYTmooc/JYTOPKYS3-data.txt", sep="\t", header=TRUE)Data after data wrangling exercises (stored locally)
#read the data from file located in your hard drive
learning2014 <- read.csv("learning2014.csv")- Questions related to the following topics were placed together:
- deep_questions , surface_questions , strategic_questions
- How to extract information from data
Since the full data set can be overwelming to explore, viewing the structure, summary and the first values of the data can be helpful to identify what are your main interests in this questionary answers.
#view the structure and summary of the non filtered "learning2014" data
str(lrn14)## 'data.frame': 183 obs. of 60 variables:
## $ Aa : int 3 2 4 4 3 4 4 3 2 3 ...
## $ Ab : int 1 2 1 2 2 2 1 1 1 2 ...
## $ Ac : int 2 2 1 3 2 1 2 2 2 1 ...
## $ Ad : int 1 2 1 2 1 1 2 1 1 1 ...
## $ Ae : int 1 1 1 1 2 1 1 1 1 1 ...
## $ Af : int 1 1 1 1 1 1 1 1 1 2 ...
## $ ST01 : int 4 4 3 3 4 4 5 4 4 4 ...
## $ SU02 : int 2 2 1 3 2 3 2 2 1 2 ...
## $ D03 : int 4 4 4 4 5 5 4 4 5 4 ...
## $ ST04 : int 4 4 4 4 3 4 2 5 5 4 ...
## $ SU05 : int 2 4 2 3 4 3 2 4 2 4 ...
## $ D06 : int 4 2 3 4 4 5 3 3 4 4 ...
## $ D07 : int 4 3 4 4 4 5 4 4 5 4 ...
## $ SU08 : int 3 4 1 2 3 4 4 2 4 2 ...
## $ ST09 : int 3 4 3 3 4 4 2 4 4 4 ...
## $ SU10 : int 2 1 1 1 2 1 1 2 1 2 ...
## $ D11 : int 3 4 4 3 4 5 5 3 4 4 ...
## $ ST12 : int 3 1 4 3 2 3 2 4 4 4 ...
## $ SU13 : int 3 3 2 2 3 1 1 2 1 2 ...
## $ D14 : int 4 2 4 4 4 5 5 4 4 4 ...
## $ D15 : int 3 3 2 3 3 4 2 2 3 4 ...
## $ SU16 : int 2 4 3 2 3 2 3 3 4 4 ...
## $ ST17 : int 3 4 3 3 4 3 4 3 4 4 ...
## $ SU18 : int 2 2 1 1 1 2 1 2 1 2 ...
## $ D19 : int 4 3 4 3 4 4 4 4 5 4 ...
## $ ST20 : int 2 1 3 3 3 3 1 4 4 2 ...
## $ SU21 : int 3 2 2 3 2 4 1 3 2 4 ...
## $ D22 : int 3 2 4 3 3 5 4 2 4 4 ...
## $ D23 : int 2 3 3 3 3 4 3 2 4 4 ...
## $ SU24 : int 2 4 3 2 4 2 2 4 2 4 ...
## $ ST25 : int 4 2 4 3 4 4 1 4 4 4 ...
## $ SU26 : int 4 4 4 2 3 2 1 4 4 4 ...
## $ D27 : int 4 2 3 3 3 5 4 4 5 4 ...
## $ ST28 : int 4 2 5 3 5 4 1 4 5 2 ...
## $ SU29 : int 3 3 2 3 3 2 1 2 1 2 ...
## $ D30 : int 4 3 4 4 3 5 4 3 4 4 ...
## $ D31 : int 4 4 3 4 4 5 4 4 5 4 ...
## $ SU32 : int 3 5 5 3 4 3 4 4 3 4 ...
## $ Ca : int 2 4 3 3 2 3 4 2 3 2 ...
## $ Cb : int 4 4 5 4 4 5 5 4 5 4 ...
## $ Cc : int 3 4 4 4 4 4 4 4 4 4 ...
## $ Cd : int 4 5 4 4 3 4 4 5 5 5 ...
## $ Ce : int 3 5 3 3 3 3 4 3 3 4 ...
## $ Cf : int 2 3 4 4 3 4 5 3 3 4 ...
## $ Cg : int 3 2 4 4 4 5 5 3 5 4 ...
## $ Ch : int 4 4 2 3 4 4 3 3 5 4 ...
## $ Da : int 3 4 1 2 3 3 2 2 4 1 ...
## $ Db : int 4 3 4 4 4 5 4 4 2 4 ...
## $ Dc : int 4 3 4 5 4 4 4 4 4 4 ...
## $ Dd : int 5 4 1 2 4 4 5 3 5 2 ...
## $ De : int 4 3 4 5 4 4 5 4 4 2 ...
## $ Df : int 2 2 1 1 2 3 1 1 4 1 ...
## $ Dg : int 4 3 3 5 5 4 4 4 5 1 ...
## $ Dh : int 3 3 1 4 5 3 4 1 4 1 ...
## $ Di : int 4 2 1 2 3 3 2 1 4 1 ...
## $ Dj : int 4 4 5 5 3 5 4 5 2 4 ...
## $ Age : int 53 55 49 53 49 38 50 37 37 42 ...
## $ Attitude: int 37 31 25 35 37 38 35 29 38 21 ...
## $ Points : int 25 12 24 10 22 21 21 31 24 26 ...
## $ gender : Factor w/ 2 levels "F","M": 1 2 1 2 2 1 2 1 2 1 ...summary(lrn14)## Aa Ab Ac Ad
## Min. :1.00 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.00 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :3.00 Median :2.000 Median :2.000 Median :1.000
## Mean :3.06 Mean :1.787 Mean :2.077 Mean :1.617
## 3rd Qu.:4.00 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :5.00 Max. :5.000 Max. :5.000 Max. :5.000
## Ae Af ST01 SU02
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:3.000 1st Qu.:2.000
## Median :1.000 Median :1.000 Median :4.000 Median :2.000
## Mean :1.437 Mean :1.579 Mean :3.765 Mean :2.612
## 3rd Qu.:1.000 3rd Qu.:2.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## D03 ST04 SU05 D06
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:4.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:3.000
## Median :4.000 Median :3.000 Median :3.000 Median :4.000
## Mean :4.361 Mean :3.213 Mean :2.874 Mean :3.448
## 3rd Qu.:5.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## D07 SU08 ST09 SU10
## Min. :1.00 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:4.00 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:1.000
## Median :4.00 Median :2.000 Median :4.000 Median :2.000
## Mean :3.94 Mean :2.508 Mean :3.224 Mean :1.995
## 3rd Qu.:5.00 3rd Qu.:3.500 3rd Qu.:4.000 3rd Qu.:2.000
## Max. :5.00 Max. :5.000 Max. :5.000 Max. :5.000
## D11 ST12 SU13 D14
## Min. :2.000 Min. :1.000 Min. :1.000 Min. :2.000
## 1st Qu.:4.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:4.000
## Median :4.000 Median :3.000 Median :2.000 Median :4.000
## Mean :3.934 Mean :2.923 Mean :2.546 Mean :4.087
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:5.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## D15 SU16 ST17 SU18
## Min. :1.000 Min. :1.000 Min. :1.00 Min. :1.000
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:3.00 1st Qu.:1.000
## Median :3.000 Median :3.000 Median :3.00 Median :1.000
## Mean :3.224 Mean :2.814 Mean :3.18 Mean :1.902
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.00 3rd Qu.:2.000
## Max. :5.000 Max. :5.000 Max. :5.00 Max. :5.000
## D19 ST20 SU21 D22
## Min. :1.00 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:3.00 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:3.000
## Median :4.00 Median :2.000 Median :2.000 Median :3.000
## Mean :3.71 Mean :2.563 Mean :2.546 Mean :3.344
## 3rd Qu.:4.00 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.00 Max. :5.000 Max. :5.000 Max. :5.000
## D23 SU24 ST25 SU26
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:4.000
## Median :3.000 Median :3.000 Median :4.000 Median :4.000
## Mean :3.137 Mean :3.055 Mean :3.339 Mean :4.126
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:5.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## D27 ST28 SU29 D30
## Min. :1.000 Min. :1.000 Min. :1.00 Min. :1.000
## 1st Qu.:3.000 1st Qu.:1.000 1st Qu.:2.00 1st Qu.:3.000
## Median :4.000 Median :2.000 Median :2.00 Median :4.000
## Mean :3.454 Mean :2.475 Mean :2.47 Mean :3.689
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:3.00 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.00 Max. :5.000
## D31 SU32 Ca Cb
## Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.000
## 1st Qu.:4.000 1st Qu.:4.00 1st Qu.:2.000 1st Qu.:4.000
## Median :4.000 Median :4.00 Median :3.000 Median :5.000
## Mean :4.022 Mean :4.06 Mean :3.011 Mean :4.372
## 3rd Qu.:5.000 3rd Qu.:5.00 3rd Qu.:4.000 3rd Qu.:5.000
## Max. :5.000 Max. :5.00 Max. :5.000 Max. :5.000
## Cc Cd Ce Cf
## Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:3.00 1st Qu.:3.500 1st Qu.:2.000
## Median :4.000 Median :4.00 Median :4.000 Median :3.000
## Mean :3.689 Mean :3.59 Mean :3.995 Mean :2.978
## 3rd Qu.:4.000 3rd Qu.:4.00 3rd Qu.:5.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.00 Max. :5.000 Max. :5.000
## Cg Ch Da Db
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:2.000 1st Qu.:4.000
## Median :4.000 Median :4.000 Median :2.000 Median :4.000
## Mean :3.852 Mean :3.667 Mean :2.568 Mean :3.874
## 3rd Qu.:5.000 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## Dc Dd De Df
## Min. :1.00 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:3.00 1st Qu.:2.000 1st Qu.:3.000 1st Qu.:1.000
## Median :4.00 Median :4.000 Median :4.000 Median :2.000
## Mean :3.71 Mean :3.301 Mean :3.475 Mean :1.847
## 3rd Qu.:4.00 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:2.000
## Max. :5.00 Max. :5.000 Max. :5.000 Max. :5.000
## Dg Dh Di Dj
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:3.000
## Median :3.000 Median :3.000 Median :2.000 Median :4.000
## Mean :2.929 Mean :2.913 Mean :2.639 Mean :3.951
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:5.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## Age Attitude Points gender
## Min. :17.00 Min. :14.00 Min. : 0.00 F:122
## 1st Qu.:21.00 1st Qu.:26.00 1st Qu.:18.00 M: 61
## Median :22.00 Median :32.00 Median :22.00
## Mean :25.58 Mean :31.21 Mean :20.61
## 3rd Qu.:27.00 3rd Qu.:37.00 3rd Qu.:26.00
## Max. :55.00 Max. :50.00 Max. :33.00head(lrn14)## Aa Ab Ac Ad Ae Af ST01 SU02 D03 ST04 SU05 D06 D07 SU08 ST09 SU10 D11
## 1 3 1 2 1 1 1 4 2 4 4 2 4 4 3 3 2 3
## 2 2 2 2 2 1 1 4 2 4 4 4 2 3 4 4 1 4
## 3 4 1 1 1 1 1 3 1 4 4 2 3 4 1 3 1 4
## 4 4 2 3 2 1 1 3 3 4 4 3 4 4 2 3 1 3
## 5 3 2 2 1 2 1 4 2 5 3 4 4 4 3 4 2 4
## 6 4 2 1 1 1 1 4 3 5 4 3 5 5 4 4 1 5
## ST12 SU13 D14 D15 SU16 ST17 SU18 D19 ST20 SU21 D22 D23 SU24 ST25 SU26
## 1 3 3 4 3 2 3 2 4 2 3 3 2 2 4 4
## 2 1 3 2 3 4 4 2 3 1 2 2 3 4 2 4
## 3 4 2 4 2 3 3 1 4 3 2 4 3 3 4 4
## 4 3 2 4 3 2 3 1 3 3 3 3 3 2 3 2
## 5 2 3 4 3 3 4 1 4 3 2 3 3 4 4 3
## 6 3 1 5 4 2 3 2 4 3 4 5 4 2 4 2
## D27 ST28 SU29 D30 D31 SU32 Ca Cb Cc Cd Ce Cf Cg Ch Da Db Dc Dd De Df Dg
## 1 4 4 3 4 4 3 2 4 3 4 3 2 3 4 3 4 4 5 4 2 4
## 2 2 2 3 3 4 5 4 4 4 5 5 3 2 4 4 3 3 4 3 2 3
## 3 3 5 2 4 3 5 3 5 4 4 3 4 4 2 1 4 4 1 4 1 3
## 4 3 3 3 4 4 3 3 4 4 4 3 4 4 3 2 4 5 2 5 1 5
## 5 3 5 3 3 4 4 2 4 4 3 3 3 4 4 3 4 4 4 4 2 5
## 6 5 4 2 5 5 3 3 5 4 4 3 4 5 4 3 5 4 4 4 3 4
## Dh Di Dj Age Attitude Points gender
## 1 3 4 4 53 37 25 F
## 2 3 2 4 55 31 12 M
## 3 1 1 5 49 25 24 F
## 4 4 2 5 53 35 10 M
## 5 5 3 3 49 37 22 M
## 6 3 3 5 38 38 21 F- View the structure and summary of the filtered “learning2014” data
## 'data.frame': 166 obs. of 8 variables:
## $ X : int 1 2 3 4 5 6 7 8 9 10 ...
## $ gender : Factor w/ 2 levels "F","M": 1 2 1 2 2 1 2 1 2 1 ...
## $ Age : int 53 55 49 53 49 38 50 37 37 42 ...
## $ Attitude: int 37 31 25 35 37 38 35 29 38 21 ...
## $ deep : num 3.58 2.92 3.5 3.5 3.67 ...
## $ stra : num 3.38 2.75 3.62 3.12 3.62 ...
## $ surf : num 2.58 3.17 2.25 2.25 2.83 ...
## $ Points : int 25 12 24 10 22 21 21 31 24 26 ...## X gender Age Attitude deep
## Min. : 1.00 F:110 Min. :17.00 Min. :14.00 Min. :1.583
## 1st Qu.: 42.25 M: 56 1st Qu.:21.00 1st Qu.:26.00 1st Qu.:3.333
## Median : 83.50 Median :22.00 Median :32.00 Median :3.667
## Mean : 83.50 Mean :25.51 Mean :31.43 Mean :3.680
## 3rd Qu.:124.75 3rd Qu.:27.00 3rd Qu.:37.00 3rd Qu.:4.083
## Max. :166.00 Max. :55.00 Max. :50.00 Max. :4.917
## stra surf Points
## Min. :1.250 Min. :1.583 Min. : 7.00
## 1st Qu.:2.625 1st Qu.:2.417 1st Qu.:19.00
## Median :3.188 Median :2.833 Median :23.00
## Mean :3.121 Mean :2.787 Mean :22.72
## 3rd Qu.:3.625 3rd Qu.:3.167 3rd Qu.:27.75
## Max. :5.000 Max. :4.333 Max. :33.00## X gender Age Attitude deep stra surf Points
## 1 1 F 53 37 3.583333 3.375 2.583333 25
## 2 2 M 55 31 2.916667 2.750 3.166667 12
## 3 3 F 49 25 3.500000 3.625 2.250000 24
## 4 4 M 53 35 3.500000 3.125 2.250000 10
## 5 5 M 49 37 3.666667 3.625 2.833333 22
## 6 6 F 38 38 4.750000 3.625 2.416667 21A careful observation of the loaded data shows you that from all the 63 original variables I filtered 7 variables of interest (Gender , Age, Attitude, Points, Deep questions, Surface questions, Strategic questions).
View data in Plots format
Graphs to visualize the overall relationships betwwen all the selected variables
Focusing on the diagonal set of graphs (7 variables by gender): You can already check that mainly in the Attitude variable the differences between gender are more noticeable;
From all the variables analysed, strategic_questions is the one that shows a more normal distributon, all the other data seems slighly to dramatically skewed.
- Based in the previous observations it seems interesting to visualize how the attitute (that seems to vary most with gender) correlates with the acquired Points.
You can verify in the graph how the correlation trend varies between female (red line) and male (blue line). The grey area in the graph shows you how this data varies.
#Linear model with three explanatory variables
my_model <- lm(formula = Points ~ Attitude + stra + surf, data = learning2014)
#Summary of the linear model
summary(my_model)##
## Call:
## lm(formula = Points ~ Attitude + stra + surf, data = learning2014)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.1550 -3.4346 0.5156 3.6401 10.8952
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.01711 3.68375 2.991 0.00322 **
## Attitude 0.33952 0.05741 5.913 1.93e-08 ***
## stra 0.85313 0.54159 1.575 0.11716
## surf -0.58607 0.80138 -0.731 0.46563
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.296 on 162 degrees of freedom
## Multiple R-squared: 0.2074, Adjusted R-squared: 0.1927
## F-statistic: 14.13 on 3 and 162 DF, p-value: 3.156e-08Analyses of the linear regression tell you that by each attitude point up the students have a chance of getting mote 0.34 points. This is the more significant relationship with the points obtained (p = 0.001)
#Linear model with three explanatory variables
my_model <- lm(formula = Points ~ Attitude, data = learning2014)
#Summary of the linear model
summary(my_model)##
## Call:
## lm(formula = Points ~ Attitude, data = learning2014)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.9763 -3.2119 0.4339 4.1534 10.6645
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.63715 1.83035 6.358 1.95e-09 ***
## Attitude 0.35255 0.05674 6.214 4.12e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.32 on 164 degrees of freedom
## Multiple R-squared: 0.1906, Adjusted R-squared: 0.1856
## F-statistic: 38.61 on 1 and 164 DF, p-value: 4.119e-09Graphical model validation
Residuals vs Fitted plot
Normal Q-Q plot
library(ggfortify)
autoplot(my_model, which= 2) +
theme_bw()
3 Logistic regression
This chapter introduces you the concept of logistic regression. Which in a very simplified matter meand how well your data fits to the idea of a linear correlation between the variables, arguments you are testing.
3.1 About this week working data set “Student Performance Data Set”.
“This data approach student achievement in secondary education of two Portuguese schools. The data attributes include student grades, demographic, social and school related features) and it was collected by using school reports and questionnaires. Two datasets are provided regarding the performance in two distinct subjects: Mathematics (mat) and Portuguese language (por). In [Cortez and Silva, 2008], the two datasets were modeled under binary/five-level classification and regression tasks (see paper source for more details).”
3.2 Load the combined data set from wrangling exercise from your local folder:
## X school sex age address famsize Pstatus Medu Fedu Mjob Fjob
## 1 1 GP F 18 U GT3 A 4 4 at_home teacher
## 2 2 GP F 17 U GT3 T 1 1 at_home other
## 3 3 GP F 15 U LE3 T 1 1 at_home other
## 4 4 GP F 15 U GT3 T 4 2 health services
## 5 5 GP F 16 U GT3 T 3 3 other other
## 6 6 GP M 16 U LE3 T 4 3 services other
## 7 7 GP M 16 U LE3 T 2 2 other other
## 8 8 GP F 17 U GT3 A 4 4 other teacher
## 9 9 GP M 15 U LE3 A 3 2 services other
## 10 10 GP M 15 U GT3 T 3 4 other other
## 11 11 GP F 15 U GT3 T 4 4 teacher health
## 12 12 GP F 15 U GT3 T 2 1 services other
## 13 13 GP M 15 U LE3 T 4 4 health services
## 14 14 GP M 15 U GT3 T 4 3 teacher other
## 15 15 GP M 15 U GT3 A 2 2 other other
## 16 16 GP F 16 U GT3 T 4 4 health other
## 17 17 GP F 16 U GT3 T 4 4 services services
## 18 18 GP F 16 U GT3 T 3 3 other other
## 19 19 GP M 17 U GT3 T 3 2 services services
## 20 20 GP M 16 U LE3 T 4 3 health other
## 21 21 GP M 15 U GT3 T 4 3 teacher other
## 22 22 GP M 15 U GT3 T 4 4 health health
## 23 23 GP M 16 U LE3 T 4 2 teacher other
## 24 24 GP M 16 U LE3 T 2 2 other other
## 25 25 GP F 15 R GT3 T 2 4 services health
## 26 26 GP F 16 U GT3 T 2 2 services services
## 27 27 GP M 15 U GT3 T 2 2 other other
## 28 28 GP M 15 U GT3 T 4 2 health services
## 29 29 GP M 16 U LE3 A 3 4 services other
## 30 30 GP M 16 U GT3 T 4 4 teacher teacher
## 31 31 GP M 15 U GT3 T 4 4 health services
## 32 32 GP M 15 U GT3 T 4 4 services services
## 33 33 GP M 15 R GT3 T 4 3 teacher at_home
## 34 34 GP M 15 U LE3 T 3 3 other other
## 35 35 GP M 16 U GT3 T 3 2 other other
## 36 36 GP F 15 U GT3 T 2 3 other other
## 37 37 GP M 15 U LE3 T 4 3 teacher services
## 38 38 GP M 16 R GT3 A 4 4 other teacher
## 39 39 GP F 15 R GT3 T 3 4 services health
## 40 40 GP F 15 R GT3 T 2 2 at_home other
## 41 41 GP F 16 U LE3 T 2 2 other other
## 42 42 GP M 15 U LE3 T 4 4 teacher other
## 43 43 GP M 15 U GT3 T 4 4 services teacher
## 44 44 GP M 15 U GT3 T 2 2 services services
## 45 45 GP F 16 U LE3 T 2 2 other at_home
## 46 46 GP F 15 U LE3 A 4 3 other other
## 47 47 GP F 16 U LE3 A 3 3 other services
## 48 48 GP M 16 U GT3 T 4 3 health services
## 49 49 GP M 15 U GT3 T 4 2 teacher other
## 50 50 GP F 15 U GT3 T 4 4 services teacher
## 51 51 GP F 16 U LE3 T 2 2 services services
## 52 52 GP F 15 U LE3 T 4 2 health other
## 53 53 GP M 15 U LE3 A 4 2 health health
## 54 54 GP F 15 U GT3 T 4 4 services services
## 55 55 GP F 15 U LE3 A 3 3 other other
## 56 56 GP F 16 U GT3 A 2 1 other other
## 57 57 GP F 15 U GT3 A 4 3 services services
## 58 58 GP M 15 U GT3 T 4 4 teacher health
## 59 59 GP M 15 U LE3 T 1 2 other at_home
## 60 60 GP F 16 U GT3 T 4 2 services other
## 61 61 GP F 16 R GT3 T 4 4 health teacher
## 62 62 GP F 16 U GT3 T 1 1 services services
## 63 63 GP F 16 U LE3 T 1 2 other services
## 64 64 GP F 16 U GT3 T 4 3 teacher health
## 65 65 GP F 15 U LE3 T 4 3 services services
## 66 66 GP F 16 U LE3 T 4 3 teacher services
## 67 67 GP M 15 U GT3 A 4 4 other services
## 68 68 GP F 16 U GT3 T 3 1 services other
## 69 69 GP F 15 R LE3 T 2 2 health services
## 70 70 GP F 15 R LE3 T 3 1 other other
## 71 71 GP M 16 U GT3 T 3 1 other other
## 72 72 GP M 15 U GT3 T 4 2 other other
## 73 73 GP F 15 R GT3 T 1 1 other other
## 74 74 GP M 16 U GT3 T 3 1 other other
## 75 75 GP F 16 U GT3 T 3 3 other services
## 76 76 GP M 15 U GT3 T 4 3 teacher other
## 77 77 GP M 15 U GT3 T 4 0 teacher other
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## reason nursery internet guardian traveltime studytime failures
## 1 course yes no mother 2 2 0
## 2 course no yes father 1 2 0
## 3 other yes yes mother 1 2 2
## 4 home yes yes mother 1 3 0
## 5 home yes no father 1 2 0
## 6 reputation yes yes mother 1 2 0
## 7 home yes yes mother 1 2 0
## 8 home yes no mother 2 2 0
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## 11 reputation yes yes mother 1 2 0
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## 26 home no yes mother 1 1 1
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## 32 reputation yes yes mother 2 2 0
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## 54 course yes yes mother 1 1 0
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## 57 reputation yes yes mother 1 2 0
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## 91 reputation yes no mother 1 2 0
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## 99 course yes no mother 1 2 0
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## 243 course yes yes mother 2 2 0
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## 276 home no no mother 1 2 0
## 277 reputation yes yes mother 2 2 0
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## 284 home yes yes mother 2 1 0
## 285 home yes yes mother 1 1 0
## 286 reputation yes no mother 2 4 0
## 287 home yes yes mother 2 2 0
## 288 home yes yes mother 2 2 0
## 289 course no yes mother 1 2 0
## 290 reputation no yes father 1 2 0
## 291 other yes yes mother 1 3 0
## 292 reputation yes yes mother 1 3 0
## 293 reputation yes yes mother 1 3 0
## 294 reputation yes yes mother 1 2 0
## 295 home yes yes mother 1 2 0
## 296 reputation yes yes mother 1 3 0
## 297 reputation yes no mother 2 4 0
## 298 reputation yes yes mother 2 3 0
## 299 home yes yes mother 1 1 0
## 300 reputation yes yes other 2 2 0
## 301 home yes yes other 2 2 0
## 302 reputation yes yes father 1 4 0
## 303 home yes yes mother 1 1 0
## 304 home yes yes mother 1 2 0
## 305 home yes yes father 2 1 0
## 306 reputation yes yes mother 2 3 0
## 307 reputation no yes father 1 4 0
## 308 course yes no other 1 1 1
## 309 reputation yes no father 1 2 0
## 310 course yes yes mother 2 2 0
## 311 course yes yes mother 1 3 0
## 312 course no yes father 1 3 0
## 313 course yes yes mother 1 2 0
## 314 course yes yes mother 1 2 0
## 315 course yes no mother 1 2 0
## 316 course yes yes mother 1 3 0
## 317 course no yes father 1 3 0
## 318 home yes yes father 2 3 0
## 319 course yes yes mother 1 3 0
## 320 reputation no yes mother 1 1 0
## 321 course yes yes mother 4 1 0
## 322 course yes yes mother 1 2 0
## 323 course yes yes mother 1 3 0
## 324 course no yes mother 2 3 0
## 325 course yes yes mother 1 4 0
## 326 course yes yes father 1 3 0
## 327 home yes yes mother 1 2 0
## 328 home no yes other 1 2 0
## 329 course yes no mother 2 4 0
## 330 course yes yes mother 1 3 0
## 331 home yes yes mother 1 2 0
## 332 home yes yes mother 1 4 0
## 333 home yes yes mother 1 2 0
## 334 home yes yes father 2 2 0
## 335 home yes yes father 1 2 0
## 336 home yes yes mother 1 2 0
## 337 home yes yes father 1 2 0
## 338 course yes yes mother 1 3 0
## 339 other yes yes mother 1 3 0
## 340 course yes yes mother 1 3 0
## 341 course yes yes mother 1 3 0
## 342 reputation yes yes mother 1 3 0
## 343 course no yes mother 2 1 0
## 344 home yes yes other 3 2 2
## 345 course yes yes mother 2 2 0
## 346 course yes yes mother 1 1 0
## 347 home yes yes other 3 1 1
## 348 home no yes mother 2 2 0
## 349 course yes no father 1 2 0
## 350 other yes yes father 2 2 0
## 351 reputation yes no mother 2 2 0
## 352 home no yes father 2 1 0
## 353 course yes yes father 2 3 0
## 354 other yes yes mother 2 2 0
## 355 course yes yes mother 1 2 0
## 356 course no no father 2 2 0
## 357 course yes no mother 2 2 0
## 358 other yes yes mother 2 3 0
## 359 reputation yes yes mother 3 1 1
## 360 course yes yes father 2 1 0
## 361 other no yes father 3 2 0
## 362 other yes yes father 3 1 0
## 363 home yes no mother 1 3 0
## 364 course yes yes mother 1 1 0
## 365 reputation yes yes mother 2 3 0
## 366 home yes yes mother 4 3 0
## 367 course yes yes mother 1 2 0
## 368 home yes yes mother 1 2 0
## 369 reputation no yes mother 1 2 0
## 370 home no yes father 1 2 0
## 371 other no yes mother 2 1 0
## 372 home yes yes father 2 2 0
## 373 other yes no mother 2 1 1
## 374 home yes no father 2 1 1
## 375 other yes no mother 2 3 0
## 376 reputation yes yes mother 3 1 0
## 377 course no yes mother 1 3 1
## 378 course yes yes mother 1 2 0
## 379 course yes no mother 2 2 2
## 380 course yes no mother 2 2 0
## 381 course no yes mother 2 1 0
## 382 course no yes mother 3 1 0
## schoolsup famsup paid activities higher romantic famrel freetime goout
## 1 yes no no no yes no 4 3 4
## 2 no yes no no yes no 5 3 3
## 3 yes no yes no yes no 4 3 2
## 4 no yes yes yes yes yes 3 2 2
## 5 no yes yes no yes no 4 3 2
## 6 no yes yes yes yes no 5 4 2
## 7 no no no no yes no 4 4 4
## 8 yes yes no no yes no 4 1 4
## 9 no yes yes no yes no 4 2 2
## 10 no yes yes yes yes no 5 5 1
## 11 no yes yes no yes no 3 3 3
## 12 no yes no yes yes no 5 2 2
## 13 no yes yes yes yes no 4 3 3
## 14 no yes yes no yes no 5 4 3
## 15 no yes no no yes yes 4 5 2
## 16 no yes no no yes no 4 4 4
## 17 no yes yes yes yes no 3 2 3
## 18 yes yes no yes yes no 5 3 2
## 19 no yes no yes yes no 5 5 5
## 20 no no yes yes yes no 3 1 3
## 21 no no no no yes no 4 4 1
## 22 no yes yes no yes no 5 4 2
## 23 no no no yes yes no 4 5 1
## 24 no yes no yes yes no 5 4 4
## 25 yes yes yes yes yes no 4 3 2
## 26 no yes yes no yes no 1 2 2
## 27 no yes yes no yes no 4 2 2
## 28 no no yes no yes no 2 2 4
## 29 yes yes no yes yes no 5 3 3
## 30 no yes yes yes yes yes 4 4 5
## 31 no yes yes no yes no 5 4 2
## 32 no yes no yes yes no 4 3 1
## 33 no yes no yes yes yes 4 5 2
## 34 no no no yes yes no 5 3 2
## 35 no yes yes no yes no 5 4 3
## 36 no yes no yes yes no 3 5 1
## 37 no yes no yes yes no 5 4 3
## 38 no yes no yes yes yes 2 4 3
## 39 yes yes yes yes yes no 4 3 2
## 40 yes yes yes yes yes no 4 3 1
## 41 no yes no yes yes yes 3 3 3
## 42 no yes no no yes yes 5 4 3
## 43 no yes no yes yes no 4 3 3
## 44 yes yes no no yes no 5 4 1
## 45 yes no no yes yes no 4 3 3
## 46 yes yes yes yes yes yes 5 2 2
## 47 no yes no no yes no 2 3 5
## 48 no no no yes yes no 4 2 2
## 49 no yes yes no yes no 4 3 3
## 50 yes yes no yes yes no 4 4 4
## 51 no yes yes no yes no 4 3 3
## 52 no yes yes no yes no 4 3 3
## 53 no no no no yes no 5 5 5
## 54 yes yes yes no yes no 3 3 4
## 55 no no yes no yes no 5 3 4
## 56 no no yes yes yes yes 5 3 4
## 57 no yes yes yes yes no 4 3 2
## 58 no yes no yes yes no 3 2 2
## 59 yes yes no yes yes no 4 3 2
## 60 no yes no no yes no 4 2 3
## 61 no yes no yes yes no 2 4 4
## 62 yes yes no yes yes yes 5 5 5
## 63 yes no no yes yes no 4 4 3
## 64 yes yes yes yes yes no 3 4 4
## 65 yes no no yes yes yes 4 4 4
## 66 no yes no yes yes no 5 4 3
## 67 no yes no yes yes yes 1 3 3
## 68 yes yes yes no yes no 4 3 3
## 69 yes yes yes no yes no 4 1 3
## 70 no yes no no yes no 4 4 2
## 71 no yes yes no yes no 4 3 2
## 72 no no no no yes no 3 3 3
## 73 yes yes no no yes yes 3 3 4
## 74 no no no yes yes no 5 3 2
## 75 yes yes yes yes yes no 4 3 3
## 76 no yes yes yes yes no 4 3 3
## 77 no no no yes yes no 3 4 3
## 78 no no yes no yes yes 5 2 3
## 79 yes yes no yes no no 4 5 1
## 80 yes yes no yes no no 4 4 3
## 81 no yes no no yes no 2 4 3
## 82 yes yes yes yes yes yes 3 2 2
## 83 yes no yes no yes no 5 3 2
## 84 no yes yes no yes no 4 4 4
## 85 no no yes yes yes no 5 3 3
## 86 no yes no yes yes no 4 3 2
## 87 no no yes no yes yes 4 4 4
## 88 no yes no no yes no 4 3 4
## 89 no yes no yes yes no 5 3 3
## 90 no no yes yes yes no 4 4 2
## 91 no yes no no yes no 4 1 3
## 92 no yes yes no yes yes 4 3 3
## 93 no no yes yes yes no 4 5 5
## 94 yes yes no no yes no 3 3 3
## 95 no yes yes yes yes no 5 3 3
## 96 no yes no yes yes no 4 3 4
## 97 yes yes yes yes yes no 3 1 2
## 98 yes yes no yes yes no 3 3 3
## 99 no yes yes no yes yes 4 3 5
## 100 no no no yes yes no 5 3 4
## 101 yes yes yes no yes no 5 3 5
## 102 yes yes yes yes yes no 4 5 5
## 103 no yes no yes yes yes 4 4 3
## 104 no yes no yes yes no 5 3 3
## 105 yes yes yes no yes no 4 3 5
## 106 no yes yes yes yes no 5 4 4
## 107 yes no no no yes no 4 3 3
## 108 yes yes yes no yes no 5 1 2
## 109 no yes no yes yes no 5 3 3
## 110 no yes no yes yes no 4 2 3
## 111 no yes yes yes yes yes 1 3 5
## 112 no yes yes yes yes yes 5 4 5
## 113 no no no yes yes no 5 5 3
## 114 yes yes no yes yes no 4 1 2
## 115 yes no no yes yes no 3 1 2
## 116 no no no no yes no 3 5 2
## 117 no no no yes yes yes 5 4 2
## 118 no yes no yes yes no 5 4 4
## 119 no yes no yes yes no 4 4 3
## 120 no yes no yes yes no 4 4 3
## 121 no no no yes yes no 5 4 2
## 122 no yes no yes yes no 5 2 4
## 123 no no no no yes no 3 4 3
## 124 no no no no yes no 3 2 3
## 125 no yes yes yes yes no 5 5 4
## 126 no yes yes yes yes yes 4 2 2
## 127 no yes no yes yes no 3 4 4
## 128 no no yes no yes yes 5 4 4
## 129 yes no no no yes no 5 5 5
## 130 yes no no yes yes yes 5 3 2
## 131 no yes no no no no 3 4 2
## 132 no no yes yes yes no 3 5 5
## 133 no yes no no yes yes 4 2 2
## 134 no yes no yes yes yes 4 3 3
## 135 no yes no no yes yes 3 4 4
## 136 no no no no yes no 3 2 1
## 137 no yes no no yes yes 5 3 3
## 138 no yes no yes yes yes 4 3 3
## 139 no no no no yes no 5 4 5
## 140 no yes no yes yes yes 4 3 2
## 141 no no no no yes yes 4 4 4
## 142 no no no yes yes no 4 3 2
## 143 yes yes no no yes no 2 2 2
## 144 no yes no yes yes no 2 3 3
## 145 no yes yes yes yes no 4 2 2
## 146 no no no no yes no 3 4 4
## 147 no yes no no yes no 4 4 3
## 148 no yes no no yes no 5 4 5
## 149 no yes yes no yes no 4 4 2
## 150 no yes no no yes no 3 3 2
## 151 no yes yes no yes no 4 3 2
## 152 no yes no no no yes 4 4 3
## 153 no yes no no no yes 3 3 2
## 154 no no no no yes no 4 5 5
## 155 no no no no no yes 2 3 5
## 156 no no no yes yes yes 4 4 4
## 157 no yes yes yes yes yes 4 2 1
## 158 no yes no no no yes 4 5 4
## 159 yes yes no no yes yes 4 2 1
## 160 yes no yes yes yes no 4 4 4
## 161 no no no no yes no 2 2 2
## 162 no yes no yes yes no 5 2 5
## 163 no no no no yes no 4 2 2
## 164 no yes yes no yes yes 4 5 5
## 165 no no no yes no yes 3 3 2
## 166 no no no yes no yes 5 3 5
## 167 no no no no no no 4 3 5
## 168 no no yes no yes yes 4 2 3
## 169 no yes yes no yes no 5 1 5
## 170 no yes yes no yes yes 4 4 2
## 171 no yes no yes yes no 3 4 5
## 172 no yes yes yes yes yes 4 3 2
## 173 no yes yes yes yes no 4 4 4
## 174 no no no yes yes yes 4 3 5
## 175 no yes yes yes yes no 4 4 5
## 176 no no yes yes yes no 4 4 4
## 177 no no yes yes yes no 3 4 4
## 178 no no no yes yes no 4 3 4
## 179 no yes no yes yes yes 4 3 3
## 180 no yes no yes yes yes 5 2 3
## 181 no yes yes yes yes no 3 4 3
## 182 no no yes yes yes yes 4 2 3
## 183 no no yes yes yes yes 4 2 3
## 184 no yes no yes yes no 5 4 2
## 185 no yes no yes yes yes 5 3 3
## 186 no yes yes no yes no 1 2 2
## 187 no yes no yes yes yes 4 3 4
## 188 no yes yes yes yes yes 3 3 3
## 189 no no yes yes yes yes 4 2 3
## 190 no yes no no yes yes 3 3 3
## 191 no no no no yes no 3 1 3
## 192 no no no no yes no 4 3 3
## 193 no no no yes yes no 5 3 3
## 194 no no yes yes yes no 4 4 4
## 195 no yes no yes yes no 4 3 2
## 196 no no no no yes no 5 3 3
## 197 no no no yes yes yes 4 3 2
## 198 no no no no yes no 5 2 3
## 199 no yes yes yes yes no 3 3 4
## 200 no yes no no yes no 4 2 4
## 201 no yes yes no yes no 4 5 2
## 202 no yes no yes yes no 4 3 5
## 203 yes yes yes yes yes no 4 4 3
## 204 no yes yes no yes no 4 4 4
## 205 no yes no no yes no 5 3 2
## 206 no yes yes yes yes no 5 3 5
## 207 no yes yes no yes yes 4 4 3
## 208 no yes yes no yes no 2 3 3
## 209 no no yes yes yes yes 1 3 2
## 210 no yes yes no yes no 4 3 2
## 211 no yes yes yes yes yes 4 4 2
## 212 no yes yes yes yes no 4 3 3
## 213 no yes yes no yes yes 5 3 5
## 214 yes yes yes no yes no 3 3 4
## 215 no yes yes yes yes no 4 4 4
## 216 no yes yes no yes no 5 2 1
## 217 no no yes no yes no 4 4 4
## 218 no no yes no yes yes 3 4 5
## 219 no yes yes no yes no 3 2 4
## 220 no yes yes no yes no 3 3 3
## 221 no yes yes yes yes no 4 3 3
## 222 no yes no yes yes no 4 2 5
## 223 no yes no yes yes yes 4 3 4
## 224 yes no no no yes no 2 3 1
## 225 no yes yes no yes no 3 3 3
## 226 no yes no yes yes no 5 3 2
## 227 no no no yes yes yes 5 3 3
## 228 no no no yes yes no 5 3 4
## 229 no yes yes no yes no 5 3 3
## 230 yes yes yes yes yes yes 4 3 2
## 231 no no no yes yes yes 3 2 3
## 232 no no no yes yes yes 3 2 3
## 233 no yes yes yes yes no 4 5 2
## 234 yes yes no yes yes yes 4 5 5
## 235 no yes yes yes yes no 4 2 4
## 236 no yes yes no yes no 3 4 2
## 237 no no no yes yes yes 5 3 3
## 238 no no yes yes yes yes 4 4 2
## 239 no no no no yes yes 4 5 2
## 240 no no no yes yes no 2 1 1
## 241 no no no no no no 5 5 4
## 242 no no no yes yes yes 2 5 5
## 243 no yes yes no yes no 3 3 3
## 244 no no no yes yes no 5 4 5
## 245 no no no yes yes no 5 3 2
## 246 no no no yes yes no 5 3 2
## 247 no yes yes no yes yes 4 4 4
## 248 no no no no yes no 4 3 3
## 249 no no no no yes no 5 2 2
## 250 no no no no no yes 5 4 5
## 251 no yes no no yes yes 4 3 3
## 252 no no yes no yes no 4 3 2
## 253 no no no no no no 4 4 5
## 254 yes yes no no yes no 5 3 3
## 255 no no no no no no 3 2 5
## 256 no no no yes yes no 3 3 2
## 257 no no no no yes no 4 4 2
## 258 no yes no yes yes no 4 4 4
## 259 no yes yes yes yes no 4 2 3
## 260 no yes no no yes no 4 3 1
## 261 no no no yes yes no 5 2 4
## 262 no no yes yes yes yes 3 4 1
## 263 no yes yes no yes yes 3 1 2
## 264 no yes yes no yes no 4 3 2
## 265 no no no yes yes no 5 3 2
## 266 no no no yes yes no 3 2 3
## 267 no yes yes yes yes yes 4 3 3
## 268 no yes yes yes yes no 4 2 5
## 269 no no yes yes yes yes 5 4 4
## 270 no no yes yes yes no 4 3 4
## 271 no yes yes yes yes yes 5 4 5
## 272 no yes no no no yes 4 3 5
## 273 no yes yes yes yes no 4 3 5
## 274 no yes yes yes yes yes 4 5 5
## 275 no yes yes no yes no 4 4 3
## 276 no yes yes yes yes yes 3 5 2
## 277 no yes yes no yes yes 4 3 3
## 278 yes yes yes no yes yes 4 4 4
## 279 no no no no no yes 4 1 1
## 280 no no yes yes yes no 3 2 4
## 281 no no yes yes yes no 4 2 4
## 282 yes yes no yes yes yes 2 4 4
## 283 no no yes yes yes no 4 2 3
## 284 no no yes yes yes yes 4 5 4
## 285 no no no no yes no 4 4 4
## 286 no yes yes yes yes no 5 2 2
## 287 yes no no yes yes no 5 4 4
## 288 yes no no yes yes no 4 4 4
## 289 no yes no no yes no 5 4 5
## 290 no no yes no yes no 4 3 3
## 291 no yes yes no yes no 4 3 3
## 292 no yes yes no yes no 4 3 3
## 293 no no yes yes yes no 4 2 4
## 294 no yes yes yes yes no 5 4 3
## 295 no yes yes yes yes yes 4 3 2
## 296 no yes yes no yes no 4 2 2
## 297 no yes yes no yes no 3 1 2
## 298 no yes yes yes yes no 5 4 2
## 299 no yes yes no yes no 4 4 3
## 300 no yes yes yes yes no 2 3 4
## 301 no yes yes no yes yes 4 4 5
## 302 no yes yes no yes no 4 3 3
## 303 no yes yes no yes yes 1 4 2
## 304 no yes no no yes yes 4 2 4
## 305 no no yes no yes no 4 1 1
## 306 no yes yes no yes no 4 3 3
## 307 no yes yes yes yes no 5 2 2
## 308 no no no yes yes no 5 5 3
## 309 no no no yes yes yes 4 5 3
## 310 no yes yes yes yes no 5 3 3
## 311 no yes yes yes yes yes 4 3 4
## 312 no yes yes yes yes no 4 3 4
## 313 no yes yes no yes no 4 4 4
## 314 no yes yes no yes yes 5 2 2
## 315 no yes no no yes yes 4 2 2
## 316 no yes yes yes yes no 3 3 2
## 317 no yes no no yes no 3 4 3
## 318 no no no no yes no 3 3 3
## 319 no no no yes yes no 4 3 3
## 320 no no no yes yes no 4 3 5
## 321 no yes no no yes no 4 4 5
## 322 no yes yes yes yes no 5 4 2
## 323 no yes yes yes yes no 5 4 4
## 324 no yes yes no yes yes 4 3 3
## 325 no yes no yes yes no 4 5 5
## 326 no yes no no yes yes 4 4 3
## 327 no no no yes yes no 5 3 4
## 328 no no no yes yes yes 4 3 3
## 329 no no no yes yes no 4 4 4
## 330 no no no no yes no 4 4 5
## 331 no yes yes no yes yes 4 3 2
## 332 no yes no no yes no 5 3 3
## 333 no yes yes no yes no 4 3 3
## 334 no yes no yes yes no 4 2 4
## 335 no yes no yes yes no 4 3 3
## 336 no no no yes yes yes 4 3 3
## 337 no yes no no yes yes 3 3 1
## 338 no yes no no yes no 4 3 3
## 339 no no no no yes yes 5 4 3
## 340 no no no no yes yes 5 3 2
## 341 no yes yes no yes yes 5 4 5
## 342 no yes yes yes yes yes 4 4 3
## 343 no yes no no yes no 2 5 5
## 344 no no no no yes no 5 4 4
## 345 no yes yes no yes no 4 5 4
## 346 no no no no no yes 4 3 3
## 347 no yes no no yes no 4 4 4
## 348 no yes yes yes yes yes 4 5 5
## 349 no yes no no yes yes 5 3 4
## 350 no yes yes yes yes no 4 3 3
## 351 no no no no yes yes 1 2 3
## 352 no no no no yes yes 3 3 2
## 353 no no no no yes no 5 3 2
## 354 no yes no no yes yes 4 3 2
## 355 no yes yes yes yes yes 2 3 4
## 356 no no no no yes no 3 2 2
## 357 no yes yes no yes no 3 3 4
## 358 no no yes no yes yes 4 2 2
## 359 no yes yes no yes yes 5 2 1
## 360 no yes yes no yes yes 5 2 3
## 361 no yes yes no yes yes 3 2 2
## 362 no yes yes yes no yes 4 3 3
## 363 no no no yes yes yes 3 4 3
## 364 no no no yes yes no 3 5 5
## 365 no no no no yes no 5 4 4
## 366 no no no no yes no 4 3 2
## 367 no no yes yes yes no 5 4 3
## 368 no no yes no yes yes 4 1 3
## 369 no yes yes yes yes no 4 5 4
## 370 no no yes yes yes no 3 2 4
## 371 no no no yes yes yes 4 4 3
## 372 no no no yes yes no 4 4 3
## 373 no no no no yes no 4 3 2
## 374 no no yes no yes no 5 4 3
## 375 no no yes no yes no 5 3 3
## 376 no yes yes yes yes yes 4 4 3
## 377 no no no yes yes no 5 4 2
## 378 no yes yes no yes no 4 3 4
## 379 no no no yes yes no 2 2 2
## 380 no no no yes yes no 1 1 1
## 381 no no no no yes no 2 4 5
## 382 no no no no yes no 4 4 1
## Dalc Walc health absences G1 G2 G3 alc_use high_use
## 1 1 1 3 5 2 8 8 1.0 FALSE
## 2 1 1 3 3 7 8 8 1.0 FALSE
## 3 2 3 3 8 10 10 11 2.5 TRUE
## 4 1 1 5 1 14 14 14 1.0 FALSE
## 5 1 2 5 2 8 12 12 1.5 FALSE
## 6 1 2 5 8 14 14 14 1.5 FALSE
## 7 1 1 3 0 12 12 12 1.0 FALSE
## 8 1 1 1 4 8 9 10 1.0 FALSE
## 9 1 1 1 0 16 17 18 1.0 FALSE
## 10 1 1 5 0 13 14 14 1.0 FALSE
## 11 1 2 2 1 12 11 12 1.5 FALSE
## 12 1 1 4 2 10 12 12 1.0 FALSE
## 13 1 3 5 1 13 14 13 2.0 FALSE
## 14 1 2 3 1 11 11 12 1.5 FALSE
## 15 1 1 3 0 14 15 16 1.0 FALSE
## 16 1 2 2 5 16 16 16 1.5 FALSE
## 17 1 2 2 8 13 14 14 1.5 FALSE
## 18 1 1 4 3 10 12 12 1.0 FALSE
## 19 2 4 5 9 7 6 6 3.0 TRUE
## 20 1 3 5 5 10 11 11 2.0 FALSE
## 21 1 1 1 0 12 14 14 1.0 FALSE
## 22 1 1 5 0 12 14 14 1.0 FALSE
## 23 1 3 5 1 14 14 15 2.0 FALSE
## 24 2 4 5 1 12 12 11 3.0 TRUE
## 25 1 1 5 2 10 10 9 1.0 FALSE
## 26 1 3 5 10 8 10 10 2.0 FALSE
## 27 1 2 5 5 12 12 12 1.5 FALSE
## 28 2 4 1 2 13 14 13 3.0 TRUE
## 29 1 1 5 3 12 12 12 1.0 FALSE
## 30 5 5 5 10 11 12 12 5.0 TRUE
## 31 3 4 5 0 10 11 12 3.5 TRUE
## 32 1 1 5 1 16 16 16 1.0 FALSE
## 33 1 1 5 0 15 15 16 1.0 FALSE
## 34 1 1 2 0 10 11 12 1.0 FALSE
## 35 1 1 5 2 12 13 14 1.0 FALSE
## 36 1 1 5 2 10 9 8 1.0 FALSE
## 37 1 1 4 1 14 15 16 1.0 FALSE
## 38 1 1 5 6 14 14 14 1.0 FALSE
## 39 1 1 5 2 12 12 12 1.0 FALSE
## 40 1 1 2 8 14 13 12 1.0 FALSE
## 41 1 2 3 20 9 10 10 1.5 FALSE
## 42 2 4 5 8 11 12 12 3.0 TRUE
## 43 1 1 5 1 16 16 16 1.0 FALSE
## 44 1 1 1 0 8 9 10 1.0 FALSE
## 45 2 2 5 14 10 10 10 2.0 FALSE
## 46 1 1 5 6 9 10 8 1.0 FALSE
## 47 1 4 3 9 12 12 12 2.5 TRUE
## 48 1 1 2 3 18 18 18 1.0 FALSE
## 49 2 2 5 3 13 14 14 2.0 FALSE
## 50 1 1 3 2 10 10 10 1.0 FALSE
## 51 2 3 4 1 13 13 13 2.5 TRUE
## 52 1 1 5 1 14 14 14 1.0 FALSE
## 53 3 4 5 5 10 10 10 3.5 TRUE
## 54 2 3 5 0 10 11 12 2.5 TRUE
## 55 4 4 1 3 12 12 13 4.0 TRUE
## 56 1 1 2 5 10 11 11 1.0 FALSE
## 57 1 1 1 0 14 14 15 1.0 FALSE
## 58 1 1 5 6 14 15 16 1.0 FALSE
## 59 1 1 5 1 12 12 12 1.0 FALSE
## 60 1 1 5 2 16 16 16 1.0 FALSE
## 61 2 3 4 3 14 14 14 2.5 TRUE
## 62 5 5 5 3 10 9 14 5.0 TRUE
## 63 1 1 1 2 10 12 10 1.0 FALSE
## 64 2 4 4 1 12 11 11 3.0 TRUE
## 65 2 4 2 0 12 11 11 3.0 TRUE
## 66 1 2 1 2 16 15 16 1.5 FALSE
## 67 5 5 3 2 12 12 12 5.0 TRUE
## 68 1 2 5 2 8 8 8 1.5 FALSE
## 69 1 3 4 1 10 10 10 2.0 FALSE
## 70 2 3 3 9 16 16 16 2.5 TRUE
## 71 1 1 5 1 13 13 13 1.0 FALSE
## 72 1 1 3 0 10 10 10 1.0 FALSE
## 73 2 4 5 2 10 8 8 3.0 TRUE
## 74 2 2 5 1 12 12 14 2.0 FALSE
## 75 2 4 5 29 11 12 11 3.0 TRUE
## 76 2 3 5 3 10 10 10 2.5 TRUE
## 77 1 1 1 4 12 11 10 1.0 FALSE
## 78 1 3 3 0 12 12 12 2.0 FALSE
## 79 1 1 3 1 8 8 10 1.0 FALSE
## 80 1 2 4 12 8 8 8 1.5 FALSE
## 81 1 2 3 13 8 8 8 1.5 FALSE
## 82 1 3 3 1 10 12 12 2.0 FALSE
## 83 1 2 5 3 10 10 10 1.5 FALSE
## 84 1 1 5 7 10 8 8 1.0 FALSE
## 85 1 3 4 3 14 14 14 2.0 FALSE
## 86 2 3 4 2 11 11 11 2.5 TRUE
## 87 2 3 5 5 10 10 10 2.5 TRUE
## 88 1 2 2 5 10 9 8 1.5 FALSE
## 89 1 3 1 4 14 14 14 2.0 FALSE
## 90 1 1 3 9 12 10 10 1.0 FALSE
## 91 3 5 5 12 8 8 8 4.0 TRUE
## 92 1 3 4 1 8 9 10 2.0 FALSE
## 93 1 3 1 5 15 15 16 2.0 FALSE
## 94 2 3 2 2 10 10 9 2.5 TRUE
## 95 1 1 1 1 12 12 12 1.0 FALSE
## 96 1 1 4 4 11 12 13 1.0 FALSE
## 97 1 1 1 3 10 12 12 1.0 FALSE
## 98 1 1 4 4 10 13 13 1.0 FALSE
## 99 1 1 5 1 10 10 11 1.0 FALSE
## 100 1 2 1 5 12 14 14 1.5 FALSE
## 101 1 1 3 1 10 11 10 1.0 FALSE
## 102 5 5 4 13 8 8 6 5.0 TRUE
## 103 1 1 4 0 16 16 16 1.0 FALSE
## 104 1 1 5 3 11 13 13 1.0 FALSE
## 105 1 1 2 21 9 8 8 1.0 FALSE
## 106 1 1 1 0 16 17 17 1.0 FALSE
## 107 1 1 4 10 10 10 10 1.0 FALSE
## 108 1 1 3 6 8 9 9 1.0 FALSE
## 109 1 1 5 3 14 16 16 1.0 FALSE
## 110 1 2 4 1 14 15 16 1.5 FALSE
## 111 3 5 1 7 11 12 12 4.0 TRUE
## 112 1 1 4 3 14 15 15 1.0 FALSE
## 113 1 1 4 5 16 16 16 1.0 FALSE
## 114 1 1 2 2 9 10 10 1.0 FALSE
## 115 1 1 5 9 9 12 12 1.0 FALSE
## 116 1 1 3 10 18 18 18 1.0 FALSE
## 117 1 1 5 6 10 9 10 1.0 FALSE
## 118 1 2 5 4 16 14 15 1.5 FALSE
## 119 2 2 5 9 12 12 12 2.0 FALSE
## 120 1 1 2 3 14 14 15 1.0 FALSE
## 121 1 1 5 3 14 14 14 1.0 FALSE
## 122 1 4 5 17 10 9 10 2.5 TRUE
## 123 1 2 4 4 14 13 14 1.5 FALSE
## 124 1 2 1 1 15 14 14 1.5 FALSE
## 125 1 2 5 6 15 14 14 1.5 FALSE
## 126 1 2 5 2 14 12 13 1.5 FALSE
## 127 1 4 5 11 13 12 13 2.5 TRUE
## 128 1 1 5 0 10 9 10 1.0 FALSE
## 129 3 2 5 1 11 11 10 2.5 TRUE
## 130 1 1 1 0 8 10 11 1.0 FALSE
## 131 1 1 5 1 8 9 10 1.0 FALSE
## 132 2 5 4 8 16 16 16 3.5 TRUE
## 133 2 2 5 0 11 6 6 2.0 FALSE
## 134 1 2 4 3 10 6 6 1.5 FALSE
## 135 1 3 5 7 12 12 12 2.0 FALSE
## 136 1 4 5 14 14 12 12 2.5 TRUE
## 137 1 1 5 1 10 6 6 1.0 FALSE
## 138 1 1 5 2 12 7 8 1.0 FALSE
## 139 2 4 5 1 10 4 5 3.0 TRUE
## 140 1 1 5 2 6 4 5 1.0 FALSE
## 141 1 3 5 0 12 11 11 2.0 FALSE
## 142 1 1 5 3 14 15 14 1.0 FALSE
## 143 1 1 3 3 8 10 6 1.0 FALSE
## 144 2 2 2 6 10 10 10 2.0 FALSE
## 145 1 1 5 2 11 12 12 1.0 FALSE
## 146 3 3 1 3 12 12 12 3.0 TRUE
## 147 1 2 4 0 7 4 5 1.5 FALSE
## 148 1 2 5 11 7 4 3 1.5 FALSE
## 149 1 2 5 0 10 12 12 1.5 FALSE
## 150 1 1 3 1 8 9 6 1.0 FALSE
## 151 1 1 5 4 12 12 12 1.0 FALSE
## 152 2 2 5 3 12 10 7 2.0 FALSE
## 153 2 1 5 8 8 8 4 1.5 FALSE
## 154 2 5 5 0 10 10 10 3.5 TRUE
## 155 2 5 4 0 8 7 0 3.5 TRUE
## 156 3 5 5 6 10 12 12 4.0 TRUE
## 157 2 3 3 5 12 12 12 2.5 TRUE
## 158 1 1 4 3 8 4 6 1.0 FALSE
## 159 1 1 4 0 12 12 12 1.0 FALSE
## 160 1 1 1 1 9 8 8 1.0 FALSE
## 161 3 3 5 11 12 10 12 3.0 TRUE
## 162 1 5 4 6 10 9 10 3.0 TRUE
## 163 1 2 3 3 14 12 13 1.5 FALSE
## 164 4 4 5 2 10 11 6 4.0 TRUE
## 165 2 2 5 4 8 7 4 2.0 FALSE
## 166 1 5 5 0 6 8 8 3.0 TRUE
## 167 2 4 4 2 10 10 10 3.0 TRUE
## 168 1 1 3 0 16 16 17 1.0 FALSE
## 169 1 1 4 0 9 10 6 1.0 FALSE
## 170 1 1 3 0 15 15 16 1.0 FALSE
## 171 2 4 2 2 8 7 5 3.0 TRUE
## 172 1 1 3 1 14 16 17 1.0 FALSE
## 173 1 3 5 0 12 10 10 2.0 FALSE
## 174 1 1 3 0 11 10 6 1.0 FALSE
## 175 1 1 4 2 12 12 12 1.0 FALSE
## 176 4 4 4 2 10 10 10 4.0 TRUE
## 177 1 4 5 1 13 12 12 2.5 TRUE
## 178 1 4 4 4 8 7 8 2.5 TRUE
## 179 3 4 3 9 10 8 10 3.5 TRUE
## 180 1 1 2 4 10 10 12 1.0 FALSE
## 181 2 3 3 7 10 9 10 2.5 TRUE
## 182 1 2 4 3 12 14 13 1.5 FALSE
## 183 1 2 3 1 12 12 12 1.5 FALSE
## 184 2 3 5 0 16 18 17 2.5 TRUE
## 185 2 3 1 44 12 11 11 2.5 TRUE
## 186 1 2 1 11 13 14 14 1.5 FALSE
## 187 2 3 4 9 12 12 12 2.5 TRUE
## 188 1 2 3 1 10 10 11 1.5 FALSE
## 189 1 2 5 0 14 14 16 1.5 FALSE
## 190 1 3 3 8 10 10 12 2.0 FALSE
## 191 1 5 3 5 8 9 10 3.0 TRUE
## 192 1 1 2 8 12 12 13 1.0 FALSE
## 193 1 1 3 0 10 10 10 1.0 FALSE
## 194 4 5 5 14 8 10 10 4.5 TRUE
## 195 3 4 5 4 10 10 10 3.5 TRUE
## 196 1 1 3 0 13 13 13 1.0 FALSE
## 197 1 1 5 4 14 15 16 1.0 FALSE
## 198 1 2 5 4 15 14 15 1.5 FALSE
## 199 3 5 3 12 10 10 11 4.0 TRUE
## 200 2 3 2 27 16 16 17 2.5 TRUE
## 201 1 2 3 0 10 10 10 1.5 FALSE
## 202 1 5 2 2 15 15 16 3.0 TRUE
## 203 1 3 4 5 10 11 11 2.0 FALSE
## 204 1 3 1 2 12 12 12 2.0 FALSE
## 205 1 2 3 20 10 10 10 1.5 FALSE
## 206 1 1 5 6 12 12 12 1.0 FALSE
## 207 3 4 5 21 9 9 8 3.5 TRUE
## 208 2 2 4 4 9 9 10 2.0 FALSE
## 209 1 1 1 7 12 14 14 1.0 FALSE
## 210 1 4 5 4 10 11 12 2.5 TRUE
## 211 1 1 4 3 9 10 10 1.0 FALSE
## 212 1 2 3 7 10 10 10 1.5 FALSE
## 213 4 5 3 14 12 12 12 4.5 TRUE
## 214 1 1 4 0 12 13 14 1.0 FALSE
## 215 2 4 5 12 9 9 10 3.0 TRUE
## 216 1 2 3 9 10 10 10 1.5 FALSE
## 217 1 3 1 2 14 16 15 2.0 FALSE
## 218 2 4 1 19 8 8 7 3.0 TRUE
## 219 2 4 4 12 8 8 9 3.0 TRUE
## 220 1 4 3 4 10 10 10 2.5 TRUE
## 221 1 1 4 2 10 11 12 1.0 FALSE
## 222 1 2 5 1 8 8 8 1.5 FALSE
## 223 1 1 5 6 9 8 6 1.0 FALSE
## 224 1 1 3 1 14 14 16 1.0 FALSE
## 225 5 5 4 4 11 11 12 5.0 TRUE
## 226 1 1 5 2 14 14 15 1.0 FALSE
## 227 1 1 4 10 8 8 8 1.0 FALSE
## 228 1 3 3 6 16 16 16 2.0 FALSE
## 229 1 3 3 1 11 11 12 2.0 FALSE
## 230 4 5 3 8 10 9 10 4.5 TRUE
## 231 1 2 3 5 14 12 14 1.5 FALSE
## 232 1 2 3 7 14 12 13 1.5 FALSE
## 233 1 1 1 2 12 12 12 1.0 FALSE
## 234 1 3 2 7 12 11 11 2.0 FALSE
## 235 2 4 1 1 14 13 14 3.0 TRUE
## 236 1 1 5 10 9 8 8 1.0 FALSE
## 237 1 3 2 5 12 10 11 2.0 FALSE
## 238 5 5 4 2 15 14 14 5.0 TRUE
## 239 1 1 5 12 11 11 11 1.0 FALSE
## 240 1 1 3 2 13 12 12 1.0 FALSE
## 241 3 5 2 8 8 7 4 4.0 TRUE
## 242 1 4 5 11 14 14 14 2.5 TRUE
## 243 2 3 4 1 11 12 12 2.5 TRUE
## 244 1 1 3 4 10 7 8 1.0 FALSE
## 245 1 2 5 0 14 12 12 1.5 FALSE
## 246 1 2 5 2 14 14 14 1.5 FALSE
## 247 1 1 3 5 10 5 6 1.0 FALSE
## 248 1 1 4 6 16 17 17 1.0 FALSE
## 249 1 1 2 3 10 12 13 1.0 FALSE
## 250 5 5 1 14 6 8 6 5.0 TRUE
## 251 1 3 5 8 6 7 8 2.0 FALSE
## 252 2 4 5 0 12 14 13 3.0 TRUE
## 253 2 4 5 4 6 8 8 3.0 TRUE
## 254 1 3 2 5 8 10 10 2.0 FALSE
## 255 2 5 5 4 6 8 7 3.5 TRUE
## 256 1 3 3 1 11 11 10 2.0 FALSE
## 257 2 4 5 0 10 12 12 3.0 TRUE
## 258 1 2 5 1 8 10 9 1.5 FALSE
## 259 1 1 4 4 14 14 15 1.0 FALSE
## 260 1 1 1 8 11 12 12 1.0 FALSE
## 261 1 2 4 5 16 15 15 1.5 FALSE
## 262 1 1 2 1 10 10 6 1.0 FALSE
## 263 1 3 2 12 16 16 16 2.0 FALSE
## 264 1 1 3 2 9 9 10 1.0 FALSE
## 265 1 1 3 2 12 12 12 1.0 FALSE
## 266 1 1 4 3 12 10 11 1.0 FALSE
## 267 1 1 3 0 10 11 6 1.0 FALSE
## 268 3 4 1 10 16 16 16 3.5 TRUE
## 269 3 4 5 1 10 10 12 3.5 TRUE
## 270 2 2 4 8 11 10 12 2.0 FALSE
## 271 1 3 5 7 10 10 12 2.0 FALSE
## 272 1 2 3 6 7 4 5 1.5 FALSE
## 273 3 3 5 16 10 10 10 3.0 TRUE
## 274 1 3 2 7 16 15 15 2.0 FALSE
## 275 1 1 3 2 12 12 12 1.0 FALSE
## 276 2 2 1 2 16 16 16 2.0 FALSE
## 277 1 1 1 4 12 13 13 1.0 FALSE
## 278 2 3 5 6 12 12 12 2.5 TRUE
## 279 1 1 5 45 11 9 10 1.0 FALSE
## 280 1 4 3 14 10 10 10 2.5 TRUE
## 281 2 3 2 11 10 10 11 2.5 TRUE
## 282 1 1 4 8 12 10 10 1.0 FALSE
## 283 1 2 1 4 10 10 10 1.5 FALSE
## 284 2 4 5 26 10 10 9 3.0 TRUE
## 285 3 4 3 18 12 11 12 3.5 TRUE
## 286 1 1 3 2 14 14 15 1.0 FALSE
## 287 1 1 4 2 10 11 12 1.0 FALSE
## 288 1 2 3 2 11 12 12 1.5 FALSE
## 289 1 2 5 8 11 10 12 1.5 FALSE
## 290 1 2 4 1 12 11 12 1.5 FALSE
## 291 1 2 2 2 18 18 18 1.5 FALSE
## 292 1 1 3 3 13 12 13 1.0 FALSE
## 293 1 3 2 3 14 14 14 2.0 FALSE
## 294 1 1 2 4 16 15 16 1.0 FALSE
## 295 1 4 5 6 14 14 14 2.5 TRUE
## 296 1 2 3 0 16 16 16 1.5 FALSE
## 297 1 1 3 3 18 18 18 1.0 FALSE
## 298 1 1 4 4 14 14 14 1.0 FALSE
## 299 1 3 5 2 14 14 13 2.0 FALSE
## 300 2 3 2 1 12 11 6 2.5 TRUE
## 301 1 2 2 5 12 11 11 1.5 FALSE
## 302 1 1 3 0 15 15 16 1.0 FALSE
## 303 2 2 1 2 17 16 16 2.0 FALSE
## 304 1 1 4 7 13 12 13 1.0 FALSE
## 305 2 2 5 0 12 12 12 2.0 FALSE
## 306 1 1 3 0 16 14 15 1.0 FALSE
## 307 1 2 5 0 18 18 18 1.5 FALSE
## 308 1 1 5 0 16 16 16 1.0 FALSE
## 309 1 2 5 0 12 11 12 1.5 FALSE
## 310 1 2 1 1 10 10 8 1.5 FALSE
## 311 1 1 5 6 12 12 13 1.0 FALSE
## 312 2 5 5 1 13 13 14 3.5 TRUE
## 313 3 3 5 1 12 11 12 3.0 TRUE
## 314 1 2 5 18 14 14 15 1.5 FALSE
## 315 1 1 3 8 12 11 11 1.0 FALSE
## 316 2 2 3 2 11 11 10 2.0 FALSE
## 317 2 3 5 0 14 16 16 2.5 TRUE
## 318 2 3 2 0 15 14 15 2.5 TRUE
## 319 2 2 3 2 11 13 12 2.0 FALSE
## 320 3 5 5 2 16 16 16 4.0 TRUE
## 321 5 5 4 5 11 10 10 5.0 TRUE
## 322 1 4 4 4 10 10 10 2.5 TRUE
## 323 1 3 4 4 12 10 11 2.0 FALSE
## 324 1 2 4 4 14 14 14 1.5 FALSE
## 325 2 4 5 1 10 10 10 3.0 TRUE
## 326 1 1 5 4 14 14 14 1.0 FALSE
## 327 1 1 4 4 8 6 6 1.0 FALSE
## 328 1 1 2 0 9 8 6 1.0 FALSE
## 329 1 1 4 3 12 11 7 1.0 FALSE
## 330 1 3 5 12 14 14 14 2.0 FALSE
## 331 2 3 2 0 10 10 8 2.5 TRUE
## 332 1 1 1 6 15 14 16 1.0 FALSE
## 333 2 3 2 2 12 12 13 2.5 TRUE
## 334 2 3 2 3 10 11 6 2.5 TRUE
## 335 2 2 2 0 11 11 6 2.0 FALSE
## 336 1 3 5 8 16 16 16 2.0 FALSE
## 337 1 2 4 9 10 10 7 1.5 FALSE
## 338 1 2 3 2 11 11 12 1.5 FALSE
## 339 2 3 1 6 14 14 16 2.5 TRUE
## 340 1 2 4 6 16 14 16 1.5 FALSE
## 341 2 3 5 0 12 12 12 2.5 TRUE
## 342 1 3 4 0 12 14 14 2.0 FALSE
## 343 5 5 5 9 10 12 12 5.0 TRUE
## 344 3 3 2 8 9 8 10 3.0 TRUE
## 345 2 3 3 3 10 11 12 2.5 TRUE
## 346 2 3 3 4 8 8 8 2.5 TRUE
## 347 3 3 5 4 8 8 9 3.0 TRUE
## 348 1 3 2 4 12 11 11 2.0 FALSE
## 349 1 1 5 0 10 10 10 1.0 FALSE
## 350 1 2 5 3 12 12 12 1.5 FALSE
## 351 1 2 5 1 14 13 13 1.5 FALSE
## 352 1 2 3 3 12 12 12 1.5 FALSE
## 353 1 1 4 0 18 16 17 1.0 FALSE
## 354 1 3 3 3 12 12 12 2.0 FALSE
## 355 1 1 1 2 16 14 15 1.0 FALSE
## 356 1 2 3 0 12 12 12 1.5 FALSE
## 357 2 4 3 2 9 10 10 3.0 TRUE
## 358 2 2 5 0 14 14 14 2.0 FALSE
## 359 1 2 1 0 8 7 4 1.5 FALSE
## 360 1 2 4 0 10 10 10 1.5 FALSE
## 361 4 2 5 5 10 8 6 3.0 TRUE
## 362 2 3 3 3 12 11 11 2.5 TRUE
## 363 1 1 3 8 12 11 12 1.0 FALSE
## 364 1 3 1 9 6 6 7 2.0 FALSE
## 365 1 1 1 0 17 18 18 1.0 FALSE
## 366 1 2 4 3 9 10 11 1.5 FALSE
## 367 3 4 2 2 10 12 12 3.5 TRUE
## 368 1 2 1 0 16 16 16 1.5 FALSE
## 369 2 3 1 14 9 10 10 2.5 TRUE
## 370 1 4 2 4 16 16 16 2.5 TRUE
## 371 1 3 5 2 7 6 4 2.0 FALSE
## 372 1 1 3 3 12 13 13 1.0 FALSE
## 373 1 3 5 0 6 6 0 2.0 FALSE
## 374 4 3 3 7 6 6 2 3.5 TRUE
## 375 1 3 4 1 12 13 12 2.0 FALSE
## 376 2 2 5 6 6 7 8 2.0 FALSE
## 377 1 2 5 2 8 8 5 1.5 FALSE
## 378 1 1 1 2 11 12 12 1.0 FALSE
## 379 2 2 5 2 6 6 4 2.0 FALSE
## 380 1 1 5 3 8 8 4 1.0 FALSE
## 381 3 4 2 4 12 13 13 3.5 TRUE
## 382 3 4 5 2 10 12 10 3.5 TRUEThe data wrangling exercise combined the two student alcohol consumption data sets. Variables not used for joining the two data have been combined by averaging (including the grade variables) - ‘alc_use’ is the average of ‘Dalc’ and ‘Walc’ - ‘high_use’ is TRUE if ‘alc_use’ is higher than 2 and FALSE otherwise
3.3 Analysis of the data
3.3.1 start by viewing the variable names, example of the first rows in the data, summary of the overall data
## [1] "X" "school" "sex" "age" "address"
## [6] "famsize" "Pstatus" "Medu" "Fedu" "Mjob"
## [11] "Fjob" "reason" "nursery" "internet" "guardian"
## [16] "traveltime" "studytime" "failures" "schoolsup" "famsup"
## [21] "paid" "activities" "higher" "romantic" "famrel"
## [26] "freetime" "goout" "Dalc" "Walc" "health"
## [31] "absences" "G1" "G2" "G3" "alc_use"
## [36] "high_use"## X school sex age address famsize Pstatus Medu Fedu Mjob Fjob
## 1 1 GP F 18 U GT3 A 4 4 at_home teacher
## 2 2 GP F 17 U GT3 T 1 1 at_home other
## 3 3 GP F 15 U LE3 T 1 1 at_home other
## 4 4 GP F 15 U GT3 T 4 2 health services
## 5 5 GP F 16 U GT3 T 3 3 other other
## 6 6 GP M 16 U LE3 T 4 3 services other
## reason nursery internet guardian traveltime studytime failures
## 1 course yes no mother 2 2 0
## 2 course no yes father 1 2 0
## 3 other yes yes mother 1 2 2
## 4 home yes yes mother 1 3 0
## 5 home yes no father 1 2 0
## 6 reputation yes yes mother 1 2 0
## schoolsup famsup paid activities higher romantic famrel freetime goout
## 1 yes no no no yes no 4 3 4
## 2 no yes no no yes no 5 3 3
## 3 yes no yes no yes no 4 3 2
## 4 no yes yes yes yes yes 3 2 2
## 5 no yes yes no yes no 4 3 2
## 6 no yes yes yes yes no 5 4 2
## Dalc Walc health absences G1 G2 G3 alc_use high_use
## 1 1 1 3 5 2 8 8 1.0 FALSE
## 2 1 1 3 3 7 8 8 1.0 FALSE
## 3 2 3 3 8 10 10 11 2.5 TRUE
## 4 1 1 5 1 14 14 14 1.0 FALSE
## 5 1 2 5 2 8 12 12 1.5 FALSE
## 6 1 2 5 8 14 14 14 1.5 FALSE## X school sex age address famsize
## Min. : 1.00 GP:342 F:198 Min. :15.00 R: 81 GT3:278
## 1st Qu.: 96.25 MS: 40 M:184 1st Qu.:16.00 U:301 LE3:104
## Median :191.50 Median :17.00
## Mean :191.50 Mean :16.59
## 3rd Qu.:286.75 3rd Qu.:17.00
## Max. :382.00 Max. :22.00
## Pstatus Medu Fedu Mjob Fjob
## A: 38 Min. :0.000 Min. :0.000 at_home : 53 at_home : 16
## T:344 1st Qu.:2.000 1st Qu.:2.000 health : 33 health : 17
## Median :3.000 Median :3.000 other :138 other :211
## Mean :2.806 Mean :2.565 services: 96 services:107
## 3rd Qu.:4.000 3rd Qu.:4.000 teacher : 62 teacher : 31
## Max. :4.000 Max. :4.000
## reason nursery internet guardian traveltime
## course :140 no : 72 no : 58 father: 91 Min. :1.000
## home :110 yes:310 yes:324 mother:275 1st Qu.:1.000
## other : 34 other : 16 Median :1.000
## reputation: 98 Mean :1.448
## 3rd Qu.:2.000
## Max. :4.000
## studytime failures schoolsup famsup paid activities
## Min. :1.000 Min. :0.0000 no :331 no :144 no :205 no :181
## 1st Qu.:1.000 1st Qu.:0.0000 yes: 51 yes:238 yes:177 yes:201
## Median :2.000 Median :0.0000
## Mean :2.037 Mean :0.2016
## 3rd Qu.:2.000 3rd Qu.:0.0000
## Max. :4.000 Max. :3.0000
## higher romantic famrel freetime goout
## no : 18 no :261 Min. :1.000 Min. :1.00 Min. :1.000
## yes:364 yes:121 1st Qu.:4.000 1st Qu.:3.00 1st Qu.:2.000
## Median :4.000 Median :3.00 Median :3.000
## Mean :3.937 Mean :3.22 Mean :3.113
## 3rd Qu.:5.000 3rd Qu.:4.00 3rd Qu.:4.000
## Max. :5.000 Max. :5.00 Max. :5.000
## Dalc Walc health absences
## Min. :1.000 Min. :1.000 Min. :1.000 Min. : 0.0
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:3.000 1st Qu.: 1.0
## Median :1.000 Median :2.000 Median :4.000 Median : 3.0
## Mean :1.482 Mean :2.296 Mean :3.573 Mean : 4.5
## 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:5.000 3rd Qu.: 6.0
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :45.0
## G1 G2 G3 alc_use
## Min. : 2.00 Min. : 4.00 Min. : 0.00 Min. :1.000
## 1st Qu.:10.00 1st Qu.:10.00 1st Qu.:10.00 1st Qu.:1.000
## Median :12.00 Median :12.00 Median :12.00 Median :1.500
## Mean :11.49 Mean :11.47 Mean :11.46 Mean :1.889
## 3rd Qu.:14.00 3rd Qu.:14.00 3rd Qu.:14.00 3rd Qu.:2.500
## Max. :18.00 Max. :18.00 Max. :18.00 Max. :5.000
## high_use
## Mode :logical
## FALSE:268
## TRUE :114
##
##
## - With this overview of the data you can basically just check one by one what are the minimum and maximum values for each variable and also the total number of female and male students in the course.
3.3.2 Another why to inspect the data is to check summaries of the data by groups of variables
##
## Attaching package: 'dplyr'## The following object is masked from 'package:GGally':
##
## nasa## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union## # A tibble: 4 x 4
## # Groups: sex [?]
## sex high_use count mean_grade
## <fctr> <lgl> <int> <dbl>
## 1 F FALSE 156 11.39744
## 2 F TRUE 42 11.71429
## 3 M FALSE 112 12.20536
## 4 M TRUE 72 10.277783.3.3 Analyse the relationship between the levels of high alcohol consuption and failure, absences, sex and grades of the students.
One could associate that an increased alcohol consuption will lead to an increase in failures, absences from school and also with a decrease in the final grades (grade form the 3rd period = G3). The differences of alcohol intake amongs sex and age seems also interesting to explore (once there is the stereotyped idea that males drink more and younger students are not leagally allowed to drink).
##
## Call:
## glm(formula = high_use ~ age + absences + sex + G3, family = "binomial",
## data = alc)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.2729 -0.8326 -0.6292 1.0442 2.1190
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.38339 1.84796 -1.831 0.067120 .
## age 0.13985 0.10328 1.354 0.175690
## absences 0.08964 0.02309 3.882 0.000104 ***
## sexM 0.98580 0.24184 4.076 4.58e-05 ***
## G3 -0.06631 0.03624 -1.830 0.067277 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 465.68 on 381 degrees of freedom
## Residual deviance: 423.66 on 377 degrees of freedom
## AIC: 433.66
##
## Number of Fisher Scoring iterations: 4## (Intercept) age absences sexM G3
## -3.38338833 0.13985344 0.08963638 0.98580237 -0.06630516failures 0.34596 0.20496 1.688 0.09142 .
absences 0.09135 0.02293 3.983 6.81e-05 sexM 0.95321 0.24278 3.926 8.63e-05 G3
3.4 Inspect numerically and graphically the distributions of the previously chosen variables and their relationship with alcohol consumption
##
##
## Cell Contents
## |-------------------------|
## | N |
## | Chi-square contribution |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 382
##
##
## | alc$age
## alc$high_use | 15 | 16 | 17 | 18 | 19 | 20 | 22 | Row Total |
## -------------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|
## FALSE | 63 | 79 | 64 | 54 | 7 | 1 | 0 | 268 |
## | 0.671 | 0.206 | 0.540 | 0.141 | 0.067 | 0.127 | 0.702 | |
## | 0.235 | 0.295 | 0.239 | 0.201 | 0.026 | 0.004 | 0.000 | 0.702 |
## | 0.778 | 0.738 | 0.640 | 0.667 | 0.636 | 1.000 | 0.000 | |
## | 0.165 | 0.207 | 0.168 | 0.141 | 0.018 | 0.003 | 0.000 | |
## -------------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|
## TRUE | 18 | 28 | 36 | 27 | 4 | 0 | 1 | 114 |
## | 1.576 | 0.484 | 1.270 | 0.331 | 0.157 | 0.298 | 1.649 | |
## | 0.158 | 0.246 | 0.316 | 0.237 | 0.035 | 0.000 | 0.009 | 0.298 |
## | 0.222 | 0.262 | 0.360 | 0.333 | 0.364 | 0.000 | 1.000 | |
## | 0.047 | 0.073 | 0.094 | 0.071 | 0.010 | 0.000 | 0.003 | |
## -------------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|
## Column Total | 81 | 107 | 100 | 81 | 11 | 1 | 1 | 382 |
## | 0.212 | 0.280 | 0.262 | 0.212 | 0.029 | 0.003 | 0.003 | |
## -------------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|
##
## You can observe that high use of alcohol didn’t alter the average final grades (G3 in the data set) of the female students, and only sligly decreases the amount of the maximum grades. As for the male students you can see a clear drop in the average grades as also the maximum grades (you can see this from the variation lines)
##
##
## Cell Contents
## |-------------------------|
## | N |
## | Chi-square contribution |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 382
##
##
## | alc$absences
## alc$high_use | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 16 | 17 | 18 | 19 | 20 | 21 | 26 | 27 | 29 | 44 | 45 | Row Total |
## -------------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|
## FALSE | 52 | 38 | 42 | 33 | 24 | 16 | 16 | 9 | 14 | 6 | 5 | 2 | 4 | 1 | 1 | 0 | 0 | 1 | 0 | 2 | 1 | 0 | 0 | 0 | 0 | 1 | 268 |
## | 0.898 | 0.138 | 0.042 | 0.624 | 0.063 | 0.021 | 0.109 | 0.040 | 0.000 | 0.695 | 0.002 | 1.160 | 0.463 | 0.116 | 3.115 | 0.702 | 0.702 | 0.116 | 0.702 | 0.254 | 0.116 | 0.702 | 0.702 | 0.702 | 0.702 | 0.127 | |
## | 0.194 | 0.142 | 0.157 | 0.123 | 0.090 | 0.060 | 0.060 | 0.034 | 0.052 | 0.022 | 0.019 | 0.007 | 0.015 | 0.004 | 0.004 | 0.000 | 0.000 | 0.004 | 0.000 | 0.007 | 0.004 | 0.000 | 0.000 | 0.000 | 0.000 | 0.004 | 0.702 |
## | 0.800 | 0.745 | 0.724 | 0.805 | 0.667 | 0.727 | 0.762 | 0.750 | 0.700 | 0.500 | 0.714 | 0.333 | 0.500 | 0.500 | 0.143 | 0.000 | 0.000 | 0.500 | 0.000 | 1.000 | 0.500 | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 | |
## | 0.136 | 0.099 | 0.110 | 0.086 | 0.063 | 0.042 | 0.042 | 0.024 | 0.037 | 0.016 | 0.013 | 0.005 | 0.010 | 0.003 | 0.003 | 0.000 | 0.000 | 0.003 | 0.000 | 0.005 | 0.003 | 0.000 | 0.000 | 0.000 | 0.000 | 0.003 | |
## -------------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|
## TRUE | 13 | 13 | 16 | 8 | 12 | 6 | 5 | 3 | 6 | 6 | 2 | 4 | 4 | 1 | 6 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 114 |
## | 2.110 | 0.324 | 0.099 | 1.466 | 0.147 | 0.049 | 0.256 | 0.094 | 0.000 | 1.634 | 0.004 | 2.726 | 1.089 | 0.272 | 7.322 | 1.649 | 1.649 | 0.272 | 1.649 | 0.597 | 0.272 | 1.649 | 1.649 | 1.649 | 1.649 | 0.298 | |
## | 0.114 | 0.114 | 0.140 | 0.070 | 0.105 | 0.053 | 0.044 | 0.026 | 0.053 | 0.053 | 0.018 | 0.035 | 0.035 | 0.009 | 0.053 | 0.009 | 0.009 | 0.009 | 0.009 | 0.000 | 0.009 | 0.009 | 0.009 | 0.009 | 0.009 | 0.000 | 0.298 |
## | 0.200 | 0.255 | 0.276 | 0.195 | 0.333 | 0.273 | 0.238 | 0.250 | 0.300 | 0.500 | 0.286 | 0.667 | 0.500 | 0.500 | 0.857 | 1.000 | 1.000 | 0.500 | 1.000 | 0.000 | 0.500 | 1.000 | 1.000 | 1.000 | 1.000 | 0.000 | |
## | 0.034 | 0.034 | 0.042 | 0.021 | 0.031 | 0.016 | 0.013 | 0.008 | 0.016 | 0.016 | 0.005 | 0.010 | 0.010 | 0.003 | 0.016 | 0.003 | 0.003 | 0.003 | 0.003 | 0.000 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.000 | |
## -------------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|
## Column Total | 65 | 51 | 58 | 41 | 36 | 22 | 21 | 12 | 20 | 12 | 7 | 6 | 8 | 2 | 7 | 1 | 1 | 2 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 382 |
## | 0.170 | 0.134 | 0.152 | 0.107 | 0.094 | 0.058 | 0.055 | 0.031 | 0.052 | 0.031 | 0.018 | 0.016 | 0.021 | 0.005 | 0.018 | 0.003 | 0.003 | 0.005 | 0.003 | 0.005 | 0.005 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | |
## -------------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|
##
## Once again the high use of alcohol didn’t alter the average number of absences of the female students, and only sligly increased the amount of the maximum number of absences (top of the box plot). As before, the alcohol consuption has more effect on the male students. You can see that the absences number increased (noticeable from the increase in the average of absences, the mimunim number of absences and maximum number of absences).
##
##
## Cell Contents
## |-------------------------|
## | N |
## | Chi-square contribution |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 382
##
##
## | alc$age
## alc$high_use | 15 | 16 | 17 | 18 | 19 | 20 | 22 | Row Total |
## -------------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|
## FALSE | 63 | 79 | 64 | 54 | 7 | 1 | 0 | 268 |
## | 0.671 | 0.206 | 0.540 | 0.141 | 0.067 | 0.127 | 0.702 | |
## | 0.235 | 0.295 | 0.239 | 0.201 | 0.026 | 0.004 | 0.000 | 0.702 |
## | 0.778 | 0.738 | 0.640 | 0.667 | 0.636 | 1.000 | 0.000 | |
## | 0.165 | 0.207 | 0.168 | 0.141 | 0.018 | 0.003 | 0.000 | |
## -------------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|
## TRUE | 18 | 28 | 36 | 27 | 4 | 0 | 1 | 114 |
## | 1.576 | 0.484 | 1.270 | 0.331 | 0.157 | 0.298 | 1.649 | |
## | 0.158 | 0.246 | 0.316 | 0.237 | 0.035 | 0.000 | 0.009 | 0.298 |
## | 0.222 | 0.262 | 0.360 | 0.333 | 0.364 | 0.000 | 1.000 | |
## | 0.047 | 0.073 | 0.094 | 0.071 | 0.010 | 0.000 | 0.003 | |
## -------------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|
## Column Total | 81 | 107 | 100 | 81 | 11 | 1 | 1 | 382 |
## | 0.212 | 0.280 | 0.262 | 0.212 | 0.029 | 0.003 | 0.003 | |
## -------------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|
##
## You can see that while the heavy alcohol consumption in the females is distributed from 16 to 17 yeard old, in the male students the high alcohol intake spreads from 16 to 18 years old. If you compare this ages with the ones from the low or non alcohol consumption, you can realize that all the male students with 17y or older are high user of alcohol.
3.5 Use logistic regression to statistically explore the relationship between chosen variables and the binary high/low alcohol consumption variable as the target variable.
##
## Call:
## glm(formula = high_use ~ age + absences + sex + G3, family = "binomial",
## data = alc)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.2729 -0.8326 -0.6292 1.0442 2.1190
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.38339 1.84796 -1.831 0.067120 .
## age 0.13985 0.10328 1.354 0.175690
## absences 0.08964 0.02309 3.882 0.000104 ***
## sexM 0.98580 0.24184 4.076 4.58e-05 ***
## G3 -0.06631 0.03624 -1.830 0.067277 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 465.68 on 381 degrees of freedom
## Residual deviance: 423.66 on 377 degrees of freedom
## AIC: 433.66
##
## Number of Fisher Scoring iterations: 4## (Intercept) age absences sexM G3
## -3.38338833 0.13985344 0.08963638 0.98580237 -0.066305163.5.1 Present and interpret the coefficients of the model as odds ratios and provide confidence intervals for them.
## Waiting for profiling to be done...## OR 2.5 % 97.5 %
## (Intercept) 0.03393229 0.0008683319 1.237502
## age 1.15010522 0.9401979286 1.410759
## absences 1.09377649 1.0474354900 1.146836
## sexM 2.67996134 1.6781593816 4.338864
## G3 0.93584524 0.8710385897 1.0044263.6 Compute the total proportion of inaccurately classified individuals (= the training error) and comment on all the results.
## age absences sex high_use probability prediction
## 1 18 5 F FALSE 0.2792297 FALSE
## 2 17 3 F FALSE 0.2197006 FALSE
## 3 15 8 F TRUE 0.2145267 FALSE
## 4 15 1 F FALSE 0.1067647 FALSE
## 5 16 2 F FALSE 0.1465247 FALSE
## 6 16 8 M FALSE 0.4082723 FALSE
## 7 16 0 M FALSE 0.2777614 FALSE
## 8 17 4 F FALSE 0.2124223 FALSE
## 9 15 0 M FALSE 0.1834303 FALSE
## 10 15 0 M FALSE 0.2265217 FALSE## prediction
## high_use FALSE TRUE
## FALSE 255 13
## TRUE 84 30You can check in the tables in how many student cases the prediction wouldn’t have assumed a correlation for high use of alcohol and the selected variables. In the 2 x 2 summary table you can see that in 84 cases the prediction claimed no relation but in the real cases you could detect a relationship between the variables. 30 cases there was in both prediction and data analysis a relation between high use of alcohol and the chosen variables.
3.7 Perform 10-fold cross-validation on your model
## [1] 0.2539267## [1] 0.2670157Performing an higher number of cross validation you can decrease the number of errors in our predictions.
3.8 Draw a graph displaying the trends of both training and testing errors by the number of predictors in the model.
## prediction
## high_use FALSE TRUE Sum
## FALSE 0.66753927 0.03403141 0.70157068
## TRUE 0.21989529 0.07853403 0.29842932
## Sum 0.88743455 0.11256545 1.00000000In this graph you can more easily evaluate how the predictions correlate with the real probability of the high use of alcohol being significantly related with the chosen variables.
4 Clustering and classification
This chapter will teach you how one can cluster and classify datasets. There is different methods to perform the clustering of the data, but in a very simple point of view you cluster what is similar. For that you can use different parameters, from simple concepts of means to more complex concepts like data populations distances.
4.1 About this week working data set “Boston”
The data set Boston is included in the library {MASS} and refers to the “Housing Values in Suburbs of Boston”. The data compiled in the dataset orginates from the following papers: Harrison and Rubinfeld (1978) & Belsley et al 1980
4.2 The data to be used in this exercise will be loaded from the library {MASS}.
##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## select## ── Attaching packages ─────────────────────────────────────── tidyverse 1.2.1 ──## ✔ tibble 1.3.4 ✔ purrr 0.2.4
## ✔ tidyr 0.7.2 ✔ stringr 1.2.0
## ✔ readr 1.1.1 ✔ forcats 0.2.0## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ✖ MASS::select() masks dplyr::select()The Boston data set includes the Housing Values in Suburbs of Boston (from 1978 - 1980). The information included in this data set includes values regarding Boston city crime, nitrogen oxide concentrations, average rooms per dwelling, lower status of the population, pupil-teacher ratio in town, etc..
## 'data.frame': 506 obs. of 14 variables:
## $ crim : num 0.00632 0.02731 0.02729 0.03237 0.06905 ...
## $ zn : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
## $ indus : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
## $ chas : int 0 0 0 0 0 0 0 0 0 0 ...
## $ nox : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
## $ rm : num 6.58 6.42 7.18 7 7.15 ...
## $ age : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
## $ dis : num 4.09 4.97 4.97 6.06 6.06 ...
## $ rad : int 1 2 2 3 3 3 5 5 5 5 ...
## $ tax : num 296 242 242 222 222 222 311 311 311 311 ...
## $ ptratio: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
## $ black : num 397 397 393 395 397 ...
## $ lstat : num 4.98 9.14 4.03 2.94 5.33 ...
## $ medv : num 24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...## [1] 506 14You can see that the data includes a total of 506 observations distributed into the following 14 variables: - crim = per capita crime rate by town. - zn = proportion of residential land zoned for lots over 25,000 sq.ft. - indus = proportion of non-retail business acres per town. - chas = Charles River dummy variable (= 1 if tract bounds river; 0 otherwise). - nox = nitrogen oxides concentration (parts per 10 million). - rm = average number of rooms per dwelling. - age = proportion of owner-occupied units built prior to 1940. - dis = weighted mean of distances to five Boston employment centres. - rad = index of accessibility to radial highways. - tax = full-value property-tax rate per $10,000. - ptratio = pupil-teacher ratio by town. - black = 1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town. - lstat = lower status of the population (percent). - medv = median value of owner-occupied homes in $1000s.
4.3 Lets have a graphical overview of the data
- From the graphical overview using the ggpairs between the variables you can start by observing which of the variables are normally distributed and which of them presented skewed data. In this data set most of the variables presented themselves skewed in either direction, being the rm (average number of rooms per dwelling) the only variable that presents a normal distribution.
4.3.1 For a better understanding of the data lets also have a look on the summaries of the variables included in this dataset.
## crim zn indus chas
## Min. : 0.00632 Min. : 0.00 Min. : 0.46 Min. :0.00000
## 1st Qu.: 0.08204 1st Qu.: 0.00 1st Qu.: 5.19 1st Qu.:0.00000
## Median : 0.25651 Median : 0.00 Median : 9.69 Median :0.00000
## Mean : 3.61352 Mean : 11.36 Mean :11.14 Mean :0.06917
## 3rd Qu.: 3.67708 3rd Qu.: 12.50 3rd Qu.:18.10 3rd Qu.:0.00000
## Max. :88.97620 Max. :100.00 Max. :27.74 Max. :1.00000
## nox rm age dis
## Min. :0.3850 Min. :3.561 Min. : 2.90 Min. : 1.130
## 1st Qu.:0.4490 1st Qu.:5.886 1st Qu.: 45.02 1st Qu.: 2.100
## Median :0.5380 Median :6.208 Median : 77.50 Median : 3.207
## Mean :0.5547 Mean :6.285 Mean : 68.57 Mean : 3.795
## 3rd Qu.:0.6240 3rd Qu.:6.623 3rd Qu.: 94.08 3rd Qu.: 5.188
## Max. :0.8710 Max. :8.780 Max. :100.00 Max. :12.127
## rad tax ptratio black
## Min. : 1.000 Min. :187.0 Min. :12.60 Min. : 0.32
## 1st Qu.: 4.000 1st Qu.:279.0 1st Qu.:17.40 1st Qu.:375.38
## Median : 5.000 Median :330.0 Median :19.05 Median :391.44
## Mean : 9.549 Mean :408.2 Mean :18.46 Mean :356.67
## 3rd Qu.:24.000 3rd Qu.:666.0 3rd Qu.:20.20 3rd Qu.:396.23
## Max. :24.000 Max. :711.0 Max. :22.00 Max. :396.90
## lstat medv
## Min. : 1.73 Min. : 5.00
## 1st Qu.: 6.95 1st Qu.:17.02
## Median :11.36 Median :21.20
## Mean :12.65 Mean :22.53
## 3rd Qu.:16.95 3rd Qu.:25.00
## Max. :37.97 Max. :50.00- From the variables summary you can mainly check the ranges of the data in the different variables. The skweded distrubition of most variables is now noticeable when you compare the Mean values and the minimum and maximum values of the data.
4.3.2 For a better understanding on how the variables relate to each other, lets visualize a correlation plot.
## corrplot 0.84 loaded## crim zn indus chas nox rm age dis rad tax
## crim 1.00 -0.20 0.41 -0.06 0.42 -0.22 0.35 -0.38 0.63 0.58
## zn -0.20 1.00 -0.53 -0.04 -0.52 0.31 -0.57 0.66 -0.31 -0.31
## indus 0.41 -0.53 1.00 0.06 0.76 -0.39 0.64 -0.71 0.60 0.72
## chas -0.06 -0.04 0.06 1.00 0.09 0.09 0.09 -0.10 -0.01 -0.04
## nox 0.42 -0.52 0.76 0.09 1.00 -0.30 0.73 -0.77 0.61 0.67
## rm -0.22 0.31 -0.39 0.09 -0.30 1.00 -0.24 0.21 -0.21 -0.29
## age 0.35 -0.57 0.64 0.09 0.73 -0.24 1.00 -0.75 0.46 0.51
## dis -0.38 0.66 -0.71 -0.10 -0.77 0.21 -0.75 1.00 -0.49 -0.53
## rad 0.63 -0.31 0.60 -0.01 0.61 -0.21 0.46 -0.49 1.00 0.91
## tax 0.58 -0.31 0.72 -0.04 0.67 -0.29 0.51 -0.53 0.91 1.00
## ptratio 0.29 -0.39 0.38 -0.12 0.19 -0.36 0.26 -0.23 0.46 0.46
## black -0.39 0.18 -0.36 0.05 -0.38 0.13 -0.27 0.29 -0.44 -0.44
## lstat 0.46 -0.41 0.60 -0.05 0.59 -0.61 0.60 -0.50 0.49 0.54
## medv -0.39 0.36 -0.48 0.18 -0.43 0.70 -0.38 0.25 -0.38 -0.47
## ptratio black lstat medv
## crim 0.29 -0.39 0.46 -0.39
## zn -0.39 0.18 -0.41 0.36
## indus 0.38 -0.36 0.60 -0.48
## chas -0.12 0.05 -0.05 0.18
## nox 0.19 -0.38 0.59 -0.43
## rm -0.36 0.13 -0.61 0.70
## age 0.26 -0.27 0.60 -0.38
## dis -0.23 0.29 -0.50 0.25
## rad 0.46 -0.44 0.49 -0.38
## tax 0.46 -0.44 0.54 -0.47
## ptratio 1.00 -0.18 0.37 -0.51
## black -0.18 1.00 -0.37 0.33
## lstat 0.37 -0.37 1.00 -0.74
## medv -0.51 0.33 -0.74 1.00
By drawing the correlation plot you can see some variables are highly positive or negatively correlated with each other.
High positive numbers (Blue) mean that variables value will shift together in the same direction. For example, when you look at the crime data, you can see its higly positvely correlated with the tax, rad and lstat variables. Meaning that the higher the index of acessibility to radial highways, the higher value of property-tax rate per $10.000, and the amount of low status of the population the bigger amount of crime you can witness on those areas.
On the other side, you can also observe some High negative numbers (Red) meaning that while the value of one variable increases the other one will decrease. For example, you can see how lstat (percentage of the lower status of the population) inversely correlates with medv (median value of owner-occupied homes in $1000s) and rm (average number of rooms per dwelling). Meaning that the higher amount of low status population the less amount of rooms per dwelling, and the less amount of owner occupied homes with the value of $1000.
4.4 Standardizing the dataset and explore the scaled data summary and how variables change.
## crim zn indus
## Min. :-0.419367 Min. :-0.48724 Min. :-1.5563
## 1st Qu.:-0.410563 1st Qu.:-0.48724 1st Qu.:-0.8668
## Median :-0.390280 Median :-0.48724 Median :-0.2109
## Mean : 0.000000 Mean : 0.00000 Mean : 0.0000
## 3rd Qu.: 0.007389 3rd Qu.: 0.04872 3rd Qu.: 1.0150
## Max. : 9.924110 Max. : 3.80047 Max. : 2.4202
## chas nox rm age
## Min. :-0.2723 Min. :-1.4644 Min. :-3.8764 Min. :-2.3331
## 1st Qu.:-0.2723 1st Qu.:-0.9121 1st Qu.:-0.5681 1st Qu.:-0.8366
## Median :-0.2723 Median :-0.1441 Median :-0.1084 Median : 0.3171
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.:-0.2723 3rd Qu.: 0.5981 3rd Qu.: 0.4823 3rd Qu.: 0.9059
## Max. : 3.6648 Max. : 2.7296 Max. : 3.5515 Max. : 1.1164
## dis rad tax ptratio
## Min. :-1.2658 Min. :-0.9819 Min. :-1.3127 Min. :-2.7047
## 1st Qu.:-0.8049 1st Qu.:-0.6373 1st Qu.:-0.7668 1st Qu.:-0.4876
## Median :-0.2790 Median :-0.5225 Median :-0.4642 Median : 0.2746
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.6617 3rd Qu.: 1.6596 3rd Qu.: 1.5294 3rd Qu.: 0.8058
## Max. : 3.9566 Max. : 1.6596 Max. : 1.7964 Max. : 1.6372
## black lstat medv
## Min. :-3.9033 Min. :-1.5296 Min. :-1.9063
## 1st Qu.: 0.2049 1st Qu.:-0.7986 1st Qu.:-0.5989
## Median : 0.3808 Median :-0.1811 Median :-0.1449
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.4332 3rd Qu.: 0.6024 3rd Qu.: 0.2683
## Max. : 0.4406 Max. : 3.5453 Max. : 2.9865## [1] "matrix"- When scaling the data, you just change the scale from which the data distributes in the x axis, not changing the values of the data itself. One can think this process is like grabbing the axis at the two ends and stretching or compressing it in order to make all your variables vary in the same comparable range, making it easier to compare. The scaling takes in account the mean (average) and standard deviation of the data.
4.4.1 Create a categorical variable of the crime rate in the Boston dataset (from the scaled crime rate). Quantiles from the old “crim”" variable will be used as the break points for the new “crime”" categorical variable.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.419367 -0.410563 -0.390280 0.000000 0.007389 9.924110## 0% 25% 50% 75% 100%
## -0.419366929 -0.410563278 -0.390280295 0.007389247 9.924109610## crime
## low med_low med_high high
## 127 126 126 127- The new crime variable is now easier to interpret the amount of data fiiting in the the new assigned labels: “low”, “med_low”, “med_high”, “high”. You can also verify how the distribution between this categories is quite even.
4.4.2 Since the new crime category looks more informative, let’s drop the old crim variable from the dataset.
## # A tibble: 506 x 14
## # Groups: crime [4]
## zn indus chas nox rm age
## * <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.28454827 -1.2866362 -0.2723291 -0.1440749 0.4132629 -0.11989477
## 2 -0.48724019 -0.5927944 -0.2723291 -0.7395304 0.1940824 0.36680343
## 3 -0.48724019 -0.5927944 -0.2723291 -0.7395304 1.2814456 -0.26554897
## 4 -0.48724019 -1.3055857 -0.2723291 -0.8344581 1.0152978 -0.80908783
## 5 -0.48724019 -1.3055857 -0.2723291 -0.8344581 1.2273620 -0.51067434
## 6 -0.48724019 -1.3055857 -0.2723291 -0.8344581 0.2068916 -0.35080997
## 7 0.04872402 -0.4761823 -0.2723291 -0.2648919 -0.3880270 -0.07015919
## 8 0.04872402 -0.4761823 -0.2723291 -0.2648919 -0.1603069 0.97784057
## 9 0.04872402 -0.4761823 -0.2723291 -0.2648919 -0.9302853 1.11638970
## 10 0.04872402 -0.4761823 -0.2723291 -0.2648919 -0.3994130 0.61548134
## # ... with 496 more rows, and 8 more variables: dis <dbl>, rad <dbl>,
## # tax <dbl>, ptratio <dbl>, black <dbl>, lstat <dbl>, medv <dbl>,
## # crime <fctr>- Now you can easily explore how the other variables vary according to the high or low crime rate category, and to have a better understanding on that I group the variables by crime categories.
4.4.3 Divide the dataset to train and test sets, so that 80% of the data belongs to the train set.
## [1] 506## zn indus chas nox rm
## 140 -0.48724019 1.56744433 -0.2723291 0.59808708 -0.190195170
## 80 -0.48724019 0.24681257 -0.2723291 -1.01568364 -0.584435480
## 228 -0.48724019 -0.71961001 -0.2723291 -0.43748771 1.250134047
## 30 -0.48724019 -0.43682573 -0.2723291 -0.14407485 0.554164692
## 306 0.92770532 -1.30558569 -0.2723291 -0.71364099 0.471616179
## 305 0.92770532 -1.30558569 -0.2723291 -0.71364099 1.354031312
## 28 -0.48724019 -0.43682573 -0.2723291 -0.14407485 -0.338213193
## 492 -0.48724019 2.42017014 -0.2723291 0.46864023 -0.429301206
## 329 -0.48724019 -1.15107469 -0.2723291 -0.81719847 -0.592974981
## 174 -0.48724019 -1.03300497 -0.2723291 -0.38570897 0.186966136
## 97 -0.48724019 -1.20209248 -0.2723291 -0.94664532 -0.173116168
## 278 1.22784527 -0.68899934 3.6647712 -0.92938574 0.770498724
## 23 -0.48724019 -0.43682573 -0.2723291 -0.14407485 -0.203004422
## 72 -0.48724019 -0.04763292 -0.2723291 -1.22279860 -0.460612711
## 162 -0.48724019 1.23072696 -0.2723291 0.43412107 1.714113616
## 383 -0.48724019 1.01499462 -0.2723291 1.25395112 -1.065494052
## 197 2.94293073 -1.40179066 -0.2723291 -1.30046671 1.426617073
## 196 2.94293073 -1.55630166 -0.2723291 -1.14513049 2.263488199
## 353 2.08538800 -1.37701059 -0.2723291 -1.24005818 -0.570202978
## 488 -0.48724019 1.01499462 -0.2723291 0.24426569 -0.540314723
## 464 -0.48724019 1.01499462 -0.2723291 1.36613839 0.325021407
## 268 0.37030254 -1.04466617 -0.2723291 0.17522737 2.864099790
## 333 1.01345959 -0.74001712 -0.2723291 -1.00791683 -0.360985196
## 262 0.37030254 -1.04466617 -0.2723291 0.79657225 1.758234373
## 60 0.58468822 -0.87557866 -0.2723291 -0.87760700 -0.509003218
## 434 -0.48724019 1.01499462 -0.2723291 1.36613839 0.215431141
## 303 0.97058245 -0.73564417 -0.2723291 -1.05020280 0.299402903
## 472 -0.48724019 1.01499462 -0.2723291 -0.19585359 -0.079181654
## 270 0.37030254 -0.60882854 3.6647712 -0.78267931 -0.518965970
## 425 -0.48724019 1.01499462 -0.2723291 0.25289548 -1.024219796
## 118 -0.48724019 -0.16424500 -0.2723291 -0.06640675 -0.375217698
## 241 0.79907391 -0.90473168 -0.2723291 -1.09335175 0.871549489
## 423 -0.48724019 1.01499462 -0.2723291 0.51178918 -0.906090028
## 315 -0.48724019 -0.18027916 -0.2723291 -0.09229612 0.401876919
## 132 -0.48724019 1.56744433 -0.2723291 0.59808708 0.058873617
## 211 -0.48724019 -0.07970124 3.6647712 -0.56693456 -0.462035961
## 68 0.04872402 -0.73855947 -0.2723291 -1.25731776 -0.578742479
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## 444 -0.48724019 1.01499462 -0.2723291 1.59914271 0.285170401
## 337 -0.48724019 -0.86683276 -0.2723291 -0.34256002 -0.591551731
## 421 -0.48724019 1.01499462 -0.2723291 1.40928733 0.179849885
## 372 -0.48724019 1.01499462 -0.2723291 0.65849561 -0.097683907
## 106 -0.48724019 -0.37560439 -0.2723291 -0.29941107 -0.617170235
## 176 -0.48724019 -1.03300497 -0.2723291 -0.38570897 0.371988664
## 189 1.44223095 -1.12192167 -0.2723291 -1.01568364 0.386221166
## 238 -0.48724019 -0.71961001 -0.2723291 -0.41159834 1.527667838
## 100 -0.48724019 -1.20209248 -0.2723291 -0.94664532 1.610216351
## 391 -0.48724019 1.01499462 -0.2723291 1.25395112 -0.813578764
## 195 2.08538800 -1.19626187 -0.2723291 -1.32635608 0.454537177
## 328 -0.48724019 -0.54760720 -0.2723291 -0.53241540 -0.286976185
## 354 3.37170210 -1.32890811 -0.2723291 -1.24868797 0.631020203
## 92 -0.48724019 -1.12629463 -0.2723291 -0.56693456 0.171310384
## 126 -0.48724019 2.11552109 -0.2723291 0.22700611 -0.425031456
## 45 -0.48724019 -0.61611679 -0.2723291 -0.92075595 -0.306901688
## 307 0.92770532 -1.30558569 -0.2723291 -0.71364099 1.615909352
## 229 -0.48724019 -0.71961001 -0.2723291 -0.43748771 1.994493909
## 290 1.76380948 -0.84788329 -0.2723291 -1.29183692 0.399030418
## 379 -0.48724019 1.01499462 -0.2723291 1.00368721 0.135729129
## 455 -0.48724019 1.01499462 -0.2723291 1.36613839 0.631020203
## 172 -0.48724019 1.23072696 -0.2723291 0.43412107 -0.575895979
## 465 -0.48724019 1.01499462 -0.2723291 0.86561057 -0.107646658
## 261 0.37030254 -1.04466617 -0.2723291 0.79657225 1.307064055
## 14 -0.48724019 -0.43682573 -0.2723291 -0.14407485 -0.477691714
## 371 -0.48724019 1.01499462 3.6647712 0.65849561 1.040916265
## 201 3.58608778 -1.40907891 -0.2723291 -1.30909650 1.210283041
## 73 -0.48724019 -0.04763292 -0.2723291 -1.22279860 -0.312594689
## 181 -0.48724019 -1.26477147 -0.2723291 -0.57556435 2.106930676
## 317 -0.48724019 -0.18027916 -0.2723291 -0.09229612 -0.527505471
## 164 -0.48724019 1.23072696 3.6647712 0.43412107 2.975113306
## 286 1.87100232 -1.29538214 -0.2723291 -1.42991356 0.239626394
## 310 -0.48724019 -0.18027916 -0.2723291 -0.09229612 -0.444956959
## 33 -0.48724019 -0.43682573 -0.2723291 -0.14407485 -0.476268464
## 369 -0.48724019 1.01499462 -0.2723291 0.65849561 -1.871053674
## 128 -0.48724019 1.56744433 -0.2723291 0.59808708 -0.842043769
## 209 -0.48724019 -0.07970124 3.6647712 -0.56693456 -0.314017939
## 399 -0.48724019 1.01499462 -0.2723291 1.19354259 -1.183623820
## 309 -0.48724019 -0.18027916 -0.2723291 -0.09229612 0.498657933
## 427 -0.48724019 1.01499462 -0.2723291 0.25289548 -0.637095738
## 63 0.58468822 -0.87557866 -0.2723291 -0.87760700 0.243896145
## 338 -0.48724019 -0.86683276 -0.2723291 -0.34256002 -0.554547225
## 480 -0.48724019 1.01499462 -0.2723291 0.51178918 -0.079181654
## 467 -0.48724019 1.01499462 -0.2723291 0.86561057 -0.473421963
## 199 2.94293073 -1.40179066 -0.2723291 -1.30046671 1.408114820
## 276 1.22784527 -0.68899934 -0.2723291 -0.92938574 0.810349730
## 473 -0.48724019 1.01499462 -0.2723291 0.21837632 0.216854391
## 324 -0.48724019 -0.54760720 -0.2723291 -0.53241540 -0.820695015
## 115 -0.48724019 -0.16424500 -0.2723291 -0.06640675 -0.043600398
## 171 -0.48724019 1.23072696 -0.2723291 0.43412107 -0.583012230
## 48 -0.48724019 -0.61611679 -0.2723291 -0.92075595 -0.362408446
## 429 -0.48724019 1.01499462 -0.2723291 1.07272553 -0.130418661
## 359 -0.48724019 1.01499462 3.6647712 1.85803641 -0.224353176
## 89 -0.48724019 -1.12629463 -0.2723291 -0.56693456 1.028107013
## 469 -0.48724019 1.01499462 -0.2723291 0.21837632 -0.510426469
## 299 2.51415937 -1.29683979 -0.2723291 -1.33498587 0.085915371
## 96 -0.48724019 -1.20209248 -0.2723291 -0.94664532 0.484425431
## 314 -0.48724019 -0.18027916 -0.2723291 -0.09229612 -0.026521396
## 102 -0.48724019 -0.37560439 -0.2723291 -0.29941107 0.706452465
## 110 -0.48724019 -0.37560439 -0.2723291 -0.29941107 -0.079181654
## 297 -0.48724019 0.40569652 -0.2723291 -1.01568364 0.376258415
## 406 -0.48724019 1.01499462 -0.2723291 1.19354259 -0.856276271
## 433 -0.48724019 1.01499462 -0.2723291 0.25289548 0.199775388
## 302 0.97058245 -0.73564417 -0.2723291 -1.05020280 0.434611674
## 142 -0.48724019 1.56744433 -0.2723291 0.59808708 -1.801314413
## 430 -0.48724019 1.01499462 -0.2723291 1.07272553 0.135729129
## 59 0.58468822 -0.87557866 -0.2723291 -0.87760700 -0.198734672
## 184 -0.48724019 -1.26477147 -0.2723291 -0.57556435 0.396183918
## 66 2.94293073 -1.13212523 -0.2723291 -1.35224545 0.007636609
## 156 -0.48724019 1.23072696 3.6647712 2.72964520 -0.188771920
## 452 -0.48724019 1.01499462 -0.2723291 1.36613839 0.527122938
## 494 -0.48724019 -0.21088983 -0.2723291 0.26152527 -0.822118266
## 240 0.79907391 -0.90473168 -0.2723291 -1.09335175 0.457383677
## 288 1.76380948 -0.84788329 -0.2723291 -1.29183692 -0.107646658
## 334 -0.48724019 -0.86683276 -0.2723291 -0.34256002 0.044641115
## 235 -0.48724019 -0.71961001 3.6647712 -0.41159834 0.628173703
## 327 -0.48724019 -0.54760720 -0.2723291 -0.53241540 0.038948114
## 7 0.04872402 -0.47618230 -0.2723291 -0.26489191 -0.388026950
## 212 -0.48724019 -0.07970124 3.6647712 -0.56693456 -1.253363081
## 502 -0.48724019 0.11562398 -0.2723291 0.15796779 0.438881424
## 335 -0.48724019 -0.86683276 -0.2723291 -0.34256002 0.036101614
## 342 1.01345959 -1.40179066 -0.2723291 -0.97253469 1.361147563
## 409 -0.48724019 1.01499462 -0.2723291 0.36508275 -0.950210785
## 407 -0.48724019 1.01499462 -0.2723291 0.90012973 -3.055197852
## 300 2.51415937 -1.29683979 -0.2723291 -1.33498587 1.076497520
## 506 -0.48724019 0.11562398 -0.2723291 0.15796779 -0.362408446
## 442 -0.48724019 1.01499462 -0.2723291 1.59914271 0.172733634
## 13 0.04872402 -0.47618230 -0.2723291 -0.26489191 -0.563086727
## 10 0.04872402 -0.47618230 -0.2723291 -0.26489191 -0.399412952
## 53 0.41317968 -0.80123846 -0.2723291 -0.99842406 0.322174907
## 215 -0.48724019 -0.07970124 -0.2723291 -0.56693456 -1.241977079
## 404 -0.48724019 1.01499462 -0.2723291 1.19354259 -1.331641842
## 133 -0.48724019 1.56744433 -0.2723291 0.59808708 0.124343127
## 311 -0.48724019 -0.18027916 -0.2723291 -0.09229612 -1.866783923
## 258 0.37030254 -1.04466617 -0.2723291 0.79657225 3.443362627
## 273 0.37030254 -0.60882854 -0.2723291 -0.78267931 0.360602663
## 375 -0.48724019 1.01499462 -0.2723291 0.97779784 -3.055197852
## 487 -0.48724019 1.01499462 -0.2723291 0.24426569 -0.242855428
## 180 -0.48724019 -1.26477147 -0.2723291 -0.57556435 0.989679257
## 87 -0.48724019 -0.96886832 -0.2723291 -0.91212616 -0.383757200
## 202 3.05012357 -1.32745046 -0.2723291 -1.20553902 -0.174539418
## 186 -0.48724019 -1.26477147 -0.2723291 -0.57556435 -0.187348670
## 304 0.97058245 -0.73564417 -0.2723291 -1.05020280 0.992525758
## 316 -0.48724019 -0.18027916 -0.2723291 -0.09229612 -0.824964766
## 260 0.37030254 -1.04466617 -0.2723291 0.79657225 0.793270728
## 47 -0.48724019 -0.61611679 -0.2723291 -0.92075595 -0.709681499
## 161 -0.48724019 1.23072696 3.6647712 0.43412107 -0.049293399
## 339 -0.48724019 -0.86683276 -0.2723291 -0.34256002 -0.321134190
## 413 -0.48724019 1.01499462 -0.2723291 0.36508275 -2.357805247
## 155 -0.48724019 1.23072696 3.6647712 2.72964520 -0.221506675
## 457 -0.48724019 1.01499462 -0.2723291 1.36613839 -0.439263958
## 168 -0.48724019 1.23072696 -0.2723291 0.43412107 -0.580165729
## 331 -0.48724019 -1.15107469 -0.2723291 -0.81719847 -0.200157922
## 113 -0.48724019 -0.16424500 -0.2723291 -0.06640675 -0.528928721
## 474 -0.48724019 1.01499462 -0.2723291 0.51178918 0.989679257
## 377 -0.48724019 1.01499462 -0.2723291 1.00368721 0.518583436
## 247 0.45605682 -0.76917014 -0.2723291 -1.06746238 -0.251394930
## 466 -0.48724019 1.01499462 -0.2723291 0.86561057 -0.748109254
## 141 -0.48724019 1.56744433 -0.2723291 0.59808708 -0.157460416
## 325 -0.48724019 -0.54760720 -0.2723291 -0.53241540 0.185542886
## 169 -0.48724019 1.23072696 -0.2723291 0.43412107 0.048910866
## 246 0.45605682 -0.76917014 -0.2723291 -1.06746238 -0.967289788
## 256 2.94293073 -1.09276866 -0.2723291 -1.40402419 -0.581588979
## 282 0.37030254 -1.13795583 -0.2723291 -0.96476788 0.972600255
## 499 -0.48724019 -0.21088983 -0.2723291 0.26152527 -0.378064199
## 67 2.94293073 -1.13212523 -0.2723291 -1.35224545 -0.708258248
## 265 0.37030254 -1.04466617 -0.2723291 0.79657225 1.311333806
## 471 -0.48724019 1.01499462 -0.2723291 0.21837632 -0.167423167
## 451 -0.48724019 1.01499462 -0.2723291 1.36613839 0.660908458
## 370 -0.48724019 1.01499462 3.6647712 0.65849561 0.566973944
## age dis rad tax ptratio
## 140 1.041786323 -1.0097983862 -0.6373311 0.17066179 1.26768382
## 80 -1.135921653 0.3360183832 -0.5224844 -0.06074124 0.11292035
## 228 0.402328842 -0.2751293639 -0.1779443 -0.60068166 -0.48755665
## 30 0.665216917 0.2108349609 -0.6373311 -0.60068166 1.17530274
## 306 -0.372125218 -0.2018524214 -0.2927910 -1.10502160 -0.02565127
## 305 -0.976057283 0.1077818401 -0.2927910 -1.10502160 -0.02565127
## 28 0.718505041 0.3126533438 -0.6373311 -0.60068166 1.17530274
## 492 1.073759197 -0.9151034909 -0.6373311 1.79641644 0.75958789
## 329 -1.519596142 0.6741465952 -0.6373311 0.12912791 -0.71850935
## 174 0.551535588 -0.5455369536 -0.5224844 -0.66594918 -0.85708096
## 97 0.036417061 -0.1423950448 -0.8670245 -0.78461740 -0.21041342
## 278 -1.455650394 0.5070770657 -0.6373311 -0.91515245 -0.39517558
## 23 0.821528746 0.0863638874 -0.6373311 -0.60068166 1.17530274
## 72 -1.814457091 0.7086717651 -0.6373311 -0.61254848 0.34387304
## 162 0.789555872 -0.8662838558 -0.5224844 -0.03107419 -1.73470120
## 383 1.116389695 -1.0517319833 1.6596029 1.52941294 0.80577843
## 197 -1.224735192 1.6687754254 -0.8670245 -0.47014661 -2.70470251
## 196 -1.299338565 0.8801578569 -0.6373311 -0.90921904 -1.87327282
## 353 -1.778931675 3.2840499862 -0.6373311 0.01639310 -0.07184181
## 488 -0.546199754 -0.3052379716 1.6596029 1.52941294 0.80577843
## 464 0.757582998 -0.4717851119 1.6596029 1.52941294 0.80577843
## 268 -0.055949019 -0.6522467981 -0.5224844 -0.85581834 -2.51994036
## 333 -1.608409681 1.3514003073 -0.9818712 -0.61848189 -0.71850935
## 262 0.739820290 -0.7860733853 -0.5224844 -0.85581834 -2.51994036
## 60 -0.759352248 1.4897384367 -0.1779443 -0.73715011 0.57482574
## 434 0.686532167 -0.7024911307 1.6596029 1.52941294 0.80577843
## 303 -1.782484217 0.8057411563 -0.2927910 -0.47014661 -1.08803366
## 472 0.786003330 -0.3304076278 1.6596029 1.52941294 0.80577843
## 270 -0.251338805 0.0581548764 -0.7521778 -1.09908819 0.06672981
## 425 0.071942477 -0.8223081923 1.6596029 1.52941294 0.80577843
## 118 0.498247464 -0.4975246471 -0.4076377 0.14099473 -0.30279450
## 241 -0.507121797 1.2067460189 -0.4076377 -0.64221553 -0.85708096
## 423 0.675874542 -0.8756393696 1.6596029 1.52941294 0.80577843
## 315 0.665216917 -0.0915333432 -0.6373311 -0.61848189 -0.02565127
## 132 1.034681240 -0.7237666137 -0.6373311 0.17066179 1.26768382
## 211 0.835738912 0.0389689498 -0.6373311 -0.77868399 0.06672981
## 68 -1.675907970 1.2836321952 -0.6373311 -0.37521203 0.20530143
## 43 -2.201684121 0.9145880470 -0.7521778 -1.03975408 -0.25660396
## 345 -1.437887686 1.2681504821 -0.5224844 -0.22687676 -0.39517558
## 194 -2.084450250 1.1514202651 -0.9818712 -0.84988492 -1.31898635
## 388 0.743372832 -1.0811757321 1.6596029 1.52941294 0.80577843
## 220 0.846396537 -0.2050342458 -0.5224844 -0.78461740 -0.94946204
## 269 -0.567515004 -0.4383522101 -0.5224844 -0.85581834 -2.51994036
## 18 0.466274590 0.2198105553 -0.6373311 -0.60068166 1.17530274
## 20 0.032864520 0.0006920764 -0.6373311 -0.60068166 1.17530274
## 61 -0.084369352 1.6290738544 -0.1779443 -0.73715011 0.57482574
## 148 0.963630408 -1.1085299245 -0.5224844 -0.03107419 -1.73470120
## 313 0.775345706 -0.4563983787 -0.6373311 -0.61848189 -0.02565127
## 52 -0.198050682 1.4340327636 -0.6373311 -0.98041997 -0.76469989
## 42 -2.333128159 0.9145880470 -0.7521778 -1.03975408 -0.25660396
## 481 -0.137657475 -0.1761128861 1.6596029 1.52941294 0.80577843
## 123 0.864159245 -0.8111955516 -0.8670245 -1.30675758 0.29768250
## 37 -0.254891346 -0.1981007179 -0.5224844 -0.76681717 0.34387304
## 418 0.729162665 -1.0198662487 1.6596029 1.52941294 0.80577843
## 231 -0.016871062 -0.0586703204 -0.1779443 -0.60068166 -0.48755665
## 352 -1.160789444 3.2840499862 -0.6373311 0.01639310 -0.07184181
## 281 -0.144762558 0.4272465145 -0.5224844 -1.14062207 -1.64232012
## 255 -1.299338565 2.5764502168 -0.9818712 -0.55321437 -0.94946204
## 384 1.116389695 -1.0741947142 1.6596029 1.52941294 0.80577843
## 56 -1.658145262 2.3277455193 -0.5224844 -1.08128796 -0.25660396
## 85 -0.730931915 0.4674704746 -0.7521778 -0.95668632 0.02053927
## 86 -0.443176049 0.3051974268 -0.7521778 -0.95668632 0.02053927
## 111 -0.503569256 -0.4830877123 -0.5224844 -0.14380900 1.12911220
## 84 -0.777114956 0.7625253315 -0.6373311 -0.75495035 0.25149196
## 193 -1.501833434 1.2749890302 -0.5224844 -0.06074124 -1.50374851
## 426 0.952972784 -0.8953951752 1.6596029 1.52941294 0.80577843
## 485 -0.947636951 -0.0337381137 1.6596029 1.52941294 0.80577843
## 160 1.116389695 -0.9636381865 -0.5224844 -0.03107419 -1.73470120
## 187 -0.531989588 -0.2829652003 -0.7521778 -1.27709053 -0.30279450
## 284 -1.555121557 0.9925190015 -0.9818712 -1.24742347 -2.24279713
## 188 -0.976057283 -0.0030596271 -0.5224844 -0.06074124 -1.50374851
## 5 -0.510674339 1.0766711351 -0.7521778 -1.10502160 0.11292035
## 398 1.077311738 -1.0265623271 1.6596029 1.52941294 0.80577843
## 420 0.281542429 -0.9502935197 1.6596029 1.52941294 0.80577843
## 344 -0.432518424 0.9199069177 -0.5224844 -0.22687676 -0.39517558
## 44 -2.205236663 0.9145880470 -0.7521778 -1.03975408 -0.25660396
## 349 -1.381047021 2.1602960705 -0.6373311 -0.76088376 -0.67231881
## 51 -0.812640371 1.4340327636 -0.6373311 -0.98041997 -0.76469989
## 222 0.807318580 -0.3547699554 -0.1779443 -0.60068166 -0.48755665
## 484 -1.004477616 0.1440166471 1.6596029 1.52941294 0.80577843
## 122 0.551535588 -0.7587191929 -0.8670245 -1.30675758 0.29768250
## 496 -1.413019895 -0.4732098094 -0.4076377 -0.10227512 0.34387304
## 477 0.889027036 -0.7074775720 1.6596029 1.52941294 0.80577843
## 137 0.885474494 -0.8681834525 -0.6373311 0.17066179 1.26768382
## 19 -1.135921653 0.0006920764 -0.6373311 -0.60068166 1.17530274
## 456 0.636796585 -0.6455032298 1.6596029 1.52941294 0.80577843
## 50 -0.233576097 1.0887810641 -0.7521778 -1.03975408 -0.25660396
## 296 -1.331311439 1.0283263992 -0.6373311 -0.70748306 -1.13422420
## 440 0.899684660 -0.9392758589 1.6596029 1.52941294 0.80577843
## 219 0.896132119 -0.4301364543 -0.5224844 -0.78461740 -0.94946204
## 69 -1.128816570 1.2836321952 -0.6373311 -0.37521203 0.20530143
## 400 0.327725469 -1.0897239172 1.6596029 1.52941294 0.80577843
## 93 -0.531989588 -0.0613297558 -0.6373311 -0.82021787 -0.11803234
## 312 -0.560409921 -0.5483863487 -0.6373311 -0.61848189 -0.02565127
## 138 1.059549031 -0.9237941458 -0.6373311 0.17066179 1.26768382
## 62 0.881921953 1.4358373805 -0.1779443 -0.73715011 0.57482574
## 340 -0.823297996 0.4830471675 -0.5224844 -1.09315478 0.80577843
## 192 -1.341969064 1.2749890302 -0.5224844 -0.06074124 -1.50374851
## 482 0.224701764 -0.2200410597 1.6596029 1.52941294 0.80577843
## 77 0.210491598 0.1221237952 -0.5224844 -0.06074124 0.11292035
## 38 -0.961847117 0.0660856927 -0.5224844 -0.76681717 0.34387304
## 173 0.707847416 -0.5693768922 -0.5224844 -0.66594918 -0.85708096
## 236 -0.251338805 -0.0679783442 -0.1779443 -0.60068166 -0.48755665
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## 302 -1.000925074 0.8057411563 -0.2927910 -0.47014661 -1.08803366
## 142 1.116389695 -1.1186927669 -0.6373311 0.17066179 1.26768382
## 430 0.960077867 -0.8675660836 1.6596029 1.52941294 0.80577843
## 59 -1.398809729 1.9089794276 -0.1779443 -0.73715011 0.57482574
## 184 0.960077867 -0.4502246894 -0.7521778 -1.27709053 -0.30279450
## 66 -1.803799466 1.3375332514 -0.6373311 -0.42267932 -1.08803366
## 156 0.498247464 -0.9733261297 -0.5224844 -0.03107419 -1.73470120
## 452 1.052443947 -0.6837801032 1.6596029 1.52941294 0.80577843
## 494 -0.517779422 -0.6711952751 -0.4076377 -0.10227512 0.34387304
## 240 -0.936979326 1.1373157596 -0.4076377 -0.64221553 -0.85708096
## 288 -1.324206356 1.6726695986 -0.4076377 -0.68374941 -0.85708096
## 334 -1.082633530 1.2648261879 -0.5224844 -1.09315478 0.80577843
## 235 -0.073711727 -0.0679783442 -0.1779443 -0.60068166 -0.48755665
## 327 -1.409467353 0.7697437989 -0.5224844 -0.71934988 0.52863520
## 7 -0.070159185 0.8384142195 -0.5224844 -0.57694801 -1.50374851
## 212 0.711399958 -0.0617571650 -0.6373311 -0.77868399 0.06672981
## 502 0.018654354 -0.6251775451 -0.9818712 -0.80241764 1.17530274
## 335 -1.068423364 1.2648261879 -0.5224844 -1.09315478 0.80577843
## 342 -0.684748875 1.5400302593 -0.9818712 -0.73715011 -1.36517689
## 409 1.041786323 -1.1114268095 1.6596029 1.52941294 0.80577843
## 407 1.116389695 -1.2427839210 1.6596029 1.52941294 0.80577843
## 300 -2.080897708 1.9151531169 -0.5224844 -0.29807769 -1.68851066
## 506 0.434301716 -0.6126402069 -0.9818712 -0.80241764 1.17530274
## 442 1.016918532 -0.8215483536 1.6596029 1.52941294 0.80577843
## 13 -1.050660656 0.7863652700 -0.5224844 -0.57694801 -1.50374851
## 10 0.615481336 1.3283202075 -0.5224844 -0.57694801 -1.50374851
## 53 -1.686565595 1.4340327636 -0.6373311 -0.98041997 -0.76469989
## 215 -2.088002791 -0.0985618510 -0.6373311 -0.77868399 0.06672981
## 404 0.974288033 -0.9936043244 1.6596029 1.52941294 0.80577843
## 133 1.041786323 -0.6969823003 -0.6373311 0.17066179 1.26768382
## 311 -1.093291155 -0.6058016588 -0.6373311 -0.61848189 -0.02565127
## 258 0.651006751 -0.9469692255 -0.5224844 -0.85581834 -2.51994036
## 273 -0.350809969 0.0581548764 -0.7521778 -1.09908819 0.06672981
## 375 1.116389695 -1.2623022771 1.6596029 1.52941294 0.80577843
## 487 0.398776300 -0.1183176566 1.6596029 1.52941294 0.80577843
## 180 -0.361467593 -0.4587728745 -0.7521778 -1.27709053 -0.30279450
## 87 -0.833955621 0.3002109855 -0.7521778 -0.95668632 0.02053927
## 202 -1.071975905 1.1753551835 -0.8670245 -0.35741180 -1.73470120
## 186 0.007996729 -0.2447358168 -0.7521778 -1.27709053 -0.30279450
## 304 -1.807352008 0.8057411563 -0.2927910 -0.47014661 -1.08803366
## 316 0.324172928 0.0712146037 -0.6373311 -0.61848189 -0.02565127
## 260 1.116389695 -0.8473828687 -0.5224844 -0.85581834 -2.51994036
## 47 -1.253155525 0.6199131095 -0.7521778 -1.03975408 -0.25660396
## 161 0.853501620 -0.9482039634 -0.5224844 -0.03107419 -1.73470120
## 339 -1.111053862 0.4830471675 -0.5224844 -1.09315478 0.80577843
## 413 1.116389695 -1.0643168114 1.6596029 1.52941294 0.80577843
## 155 0.974288033 -0.9714740229 -0.5224844 -0.03107419 -1.73470120
## 457 0.686532167 -0.5767378294 1.6596029 1.52941294 0.80577843
## 168 0.377461051 -0.6502047316 -0.5224844 -0.03107419 -1.73470120
## 331 -1.292233482 0.9871051509 -0.6373311 0.12912791 -0.71850935
## 113 0.864159245 -0.6846349217 -0.4076377 0.14099473 -0.30279450
## 474 -0.034633770 -0.5993905200 1.6596029 1.52941294 0.80577843
## 377 0.878369411 -1.1635707388 1.6596029 1.52941294 0.80577843
## 247 -1.196314860 2.0232876588 -0.2927910 -0.46421320 0.29768250
## 466 -0.723826832 -0.3459843207 1.6596029 1.52941294 0.80577843
## 141 0.889027036 -1.0367726593 -0.6373311 0.17066179 1.26768382
## 325 -1.011582699 0.4397838527 -0.5224844 -0.71934988 0.52863520
## 169 0.977840575 -0.8049743725 -0.5224844 -0.03107419 -1.73470120
## 246 0.057732311 1.9755128019 -0.2927910 -0.46421320 0.29768250
## 256 -1.757616426 2.5764502168 -0.9818712 -0.55321437 -0.94946204
## 282 -1.114606404 0.6884410603 -0.5224844 -1.14062207 -1.64232012
## 499 -0.116342226 -0.6581830377 -0.4076377 -0.10227512 0.34387304
## 67 -1.331311439 1.3375332514 -0.6373311 -0.42267932 -1.08803366
## 265 0.817976204 -0.8856597421 -0.5224844 -0.85581834 -2.51994036
## 471 0.547983046 -0.3617034834 1.6596029 1.52941294 0.80577843
## 451 0.853501620 -0.6987869171 1.6596029 1.52941294 0.80577843
## 370 1.002708366 -1.1579669285 1.6596029 1.52941294 0.80577843
## black lstat medv crime
## 140 0.44061589 0.813175569 -0.514597451 med_high
## 80 0.43141494 -0.497553933 -0.242772758 med_low
## 228 0.16874956 -0.881250390 0.985874857 med_high
## 30 0.25802074 -0.094252548 -0.166661844 med_high
## 306 0.40184044 -0.521359918 0.637939249 low
## 305 0.40534556 -0.801430324 1.475159305 low
## 28 -0.55089661 0.647934029 -0.840787084 med_high
## 492 0.36624150 0.758561840 -0.971262937 med_low
## 329 0.28222802 -0.375723306 -0.351502635 low
## 174 0.42528097 -0.505956045 0.116035838 med_low
## 97 0.38508156 -0.183875078 -0.123169893 med_low
## 278 0.40282626 -1.189327837 1.148969673 low
## 23 0.44061589 0.849584722 -0.797295133 med_high
## 72 0.22198366 -0.388326475 -0.090550930 med_low
## 162 0.19449033 -1.529613381 2.986504601 med_high
## 383 0.44061589 1.532956514 -1.221341655 high
## 197 0.44061589 -1.200530653 1.170715648 low
## 196 0.41137000 -1.355969729 2.986504601 low
## 353 0.39055831 -0.681000049 -0.427613550 low
## 488 0.34553935 -0.168471205 -0.210153795 high
## 464 0.40687906 -0.330912041 -0.253645746 high
## 268 0.30523040 -0.730012370 2.986504601 med_high
## 333 0.06107647 -0.675398641 -0.340629648 low
## 262 0.34718238 -0.755218707 2.236268447 med_high
## 60 0.44061589 -0.480749709 -0.318883672 med_low
## 434 -2.80940262 0.499496714 -0.895152022 high
## 303 0.29504363 -0.557769070 0.420479494 med_low
## 472 0.42341887 0.030378783 -0.318883672 high
## 270 0.37971433 0.139606242 -0.199280807 med_low
## 425 -3.86685532 0.631129805 -1.177849704 high
## 118 0.41443699 -0.329511689 -0.362375623 med_low
## 241 0.37872851 -0.178273670 -0.057931966 med_low
## 423 -0.71333730 0.202622083 -0.188407819 high
## 315 0.42736214 -0.472347596 0.137781813 med_high
## 132 0.44061589 -0.055042691 -0.318883672 med_high
## 211 0.40063555 0.646533677 -0.090550930 med_low
## 68 0.43305797 -0.637589136 -0.057931966 low
## 43 0.29241479 -0.958269752 0.300876629 med_low
## 345 0.34280097 -1.126311996 0.942382906 low
## 194 0.40194997 -1.067497210 0.931509918 low
## 388 0.44061589 2.707851869 -1.645388177 high
## 220 0.40600278 -0.301504649 0.050797911 med_low
## 269 0.36832267 -1.329363040 2.279760398 med_high
## 18 0.32943768 0.282442149 -0.547216415 med_high
## 20 0.37544246 -0.192277190 -0.471105500 med_high
## 61 0.42100910 0.069588640 -0.416740562 med_low
## 148 0.38376713 2.363365269 -0.862533059 med_high
## 313 0.43404378 -0.130661701 -0.340629648 med_high
## 52 0.40852209 -0.451342316 -0.221026782 low
## 42 0.31475997 -1.094103899 0.442225470 med_low
## 481 0.44061589 -0.267896200 0.050797911 high
## 123 0.23458021 0.738956911 -0.221026782 med_low
## 37 0.22877484 -0.174072614 -0.275391721 med_low
## 418 -2.51179552 1.958663532 -1.319198544 high
## 231 0.23742812 -0.140464165 0.192146752 med_high
## 352 0.15450999 -1.003081017 0.170400776 low
## 281 0.33557165 -1.245341918 2.486347165 low
## 255 0.39669229 -0.851842997 -0.068804954 low
## 384 0.44061589 1.667390309 -1.112611777 high
## 56 0.42999098 -1.098304955 1.399048391 low
## 85 0.44061589 -0.424735627 0.148654801 low
## 86 0.39022971 -0.857444405 0.442225470 low
## 111 0.40326440 0.048583360 -0.090550930 med_low
## 84 0.37204687 -0.720209906 0.039924923 low
## 193 0.37040384 -1.369973249 1.507778268 med_low
## 426 -3.82271264 1.643584324 -1.547531287 high
## 485 0.15396231 0.096195329 -0.210153795 med_high
## 160 0.08364072 -0.737014131 0.083416874 med_high
## 187 0.39384437 -1.148717628 2.986504601 low
## 284 0.42550004 -1.329363040 2.986504601 low
## 188 0.40742673 -0.836439125 1.029366808 low
## 5 0.44061589 -1.025486649 1.486032293 low
## 398 0.39899252 1.017626966 -1.525785311 high
## 420 -3.37613768 1.412526239 -1.536658299 high
## 344 0.44061589 -0.766421523 0.148654801 low
## 44 0.41388931 -0.730012370 0.235638703 med_low
## 349 0.37533292 -0.933063415 0.213892727 low
## 51 0.42593818 0.111599201 -0.308010684 med_low
## 222 0.42243305 1.233281179 -0.090550930 med_high
## 484 0.39702089 -0.312707465 -0.079677942 med_high
## 122 0.22997973 0.226428068 -0.242772758 low
## 496 0.40107369 0.692745294 0.061670899 med_low
## 477 0.43305797 0.843983314 -0.634200317 high
## 137 0.23633277 0.594720652 -0.558089402 med_high
## 19 -0.74137830 -0.134862757 -0.253645746 med_high
## 456 -3.34908249 0.766963952 -0.916897998 high
## 50 0.44061589 0.496696010 -0.340629648 med_low
## 296 0.44061589 -0.893853558 0.659685225 med_low
## 440 0.44061589 1.432131167 -1.058246839 high
## 219 0.44061589 0.737556559 -0.112296905 med_low
## 69 0.44061589 0.061186528 -0.558089402 med_low
## 400 -0.20279379 2.424980758 -1.764991042 high
## 93 0.41991374 -0.629187024 0.039924923 low
## 312 0.44061589 -0.934463767 -0.047058979 med_high
## 138 0.40972697 0.271239333 -0.590708366 med_high
## 62 0.23447067 0.250234052 -0.710311231 med_low
## 340 0.44061589 -0.407931403 -0.384121599 low
## 192 0.36186010 -1.115109179 0.866271992 low
## 482 0.39866392 -0.688001809 0.126908825 high
## 77 0.18605612 -0.095652900 -0.275391721 med_low
## 38 0.44061589 -0.543765550 -0.166661844 low
## 173 0.44061589 0.285242853 0.061670899 med_low
## 236 0.21990249 -0.248291271 0.159527789 med_high
## 330 0.20303408 -0.744015891 0.007305960 low
## 124 0.14936183 1.786420232 -0.568962390 med_low
## 218 0.39548740 -0.414933163 0.670558212 low
## 435 -2.80458308 0.352459751 -1.177849704 high
## 116 -0.12885754 0.435080520 -0.460232513 med_low
## 392 0.23775673 0.855186130 0.072543887 high
## 253 0.32220836 -1.277550015 0.768415102 med_low
## 437 -3.60572343 0.755761136 -1.406182446 high
## 361 0.19591429 -0.681000049 0.268257666 high
## 410 -1.94221255 0.998022037 0.540082359 high
## 438 -3.80474886 1.932056843 -1.504039336 high
## 254 0.44061589 -1.276149663 2.203649484 med_high
## 207 0.41838025 -0.235688103 0.203019739 med_low
## 39 0.40260719 -0.353317674 0.235638703 med_low
## 79 0.32560395 -0.043839875 -0.144915868 low
## 40 0.42670493 -1.166922204 0.898890955 low
## 504 0.44061589 -0.982075736 0.148654801 low
## 214 0.31914137 -0.458344076 0.605320286 med_low
## 412 -3.52291483 1.199672730 -0.579835378 high
## 432 -3.01598599 0.985418869 -0.916897998 high
## 271 0.35024937 0.048583360 -0.155788856 med_high
## 272 0.44061589 -0.849042293 0.290003641 med_low
## 82 0.42670493 -0.760820115 0.148654801 low
## 291 0.44061589 -1.305557056 0.648812237 low
## 234 0.24400024 -1.218735230 2.801663810 med_high
## 76 0.29088130 -0.519959566 -0.123169893 med_low
## 242 0.41564187 -0.035437762 -0.264518733 med_low
## 147 -2.05273356 0.559711851 -0.753803182 med_high
## 415 -2.93996857 3.406627533 -1.688880128 high
## 486 0.34992076 -0.290301832 -0.144915868 med_high
## 117 0.40118323 -0.085850436 -0.144915868 med_low
## 411 -3.87835651 -0.356118378 -0.819041108 high
## 491 -0.41890671 2.384370549 -1.569277262 med_low
## 346 0.31727927 -0.297303592 -0.547216415 low
## 267 0.30008225 0.299246373 0.888017967 med_high
## 436 -2.70359163 1.486744897 -0.993008912 high
## 501 0.44061589 0.234830180 -0.623327329 med_low
## 163 0.36076474 -1.503006692 2.986504601 med_high
## 395 0.44061589 0.517701290 -1.069119826 high
## 318 0.44061589 0.460286857 -0.297137697 med_low
## 55 0.44061589 0.300646725 -0.394994586 low
## 405 -0.29808940 2.062289582 -1.525785311 high
## 9 0.32812326 2.419379350 -0.655946292 med_low
## 88 0.42144724 -0.589977167 -0.036185991 low
## 135 -1.02868910 0.652135085 -0.753803182 med_high
## 178 0.42637632 -0.891052854 0.224765715 low
## 232 0.21322085 -1.036689465 0.996747845 med_high
## 99 0.40370254 -1.271948607 2.312379361 low
## 22 0.39274902 0.164812578 -0.318883672 med_high
## 4 0.41575141 -1.360170785 1.181588636 low
## 83 0.44061589 -0.830837717 0.246511690 low
## 81 0.44061589 -1.031088057 0.594447298 low
## 154 -1.03756145 0.439281577 -0.340629648 med_high
## 293 0.44061589 -1.113708827 0.583574310 low
## 249 0.19755732 -0.438739148 0.213892727 med_low
## 326 0.40534556 -1.060495450 0.224765715 med_low
## 35 -1.18696744 1.076441751 -0.982135924 med_high
## 424 -3.87923279 1.489545601 -0.993008912 high
## 71 0.29635805 -0.830837717 0.181273764 med_low
## 34 0.02295823 0.797771697 -1.025627875 med_high
## 363 0.26415471 -0.344915562 -0.188407819 high
## 130 0.44061589 0.796371345 -0.895152022 med_high
## 453 0.31125484 0.646533677 -0.699438243 high
## 343 0.36459848 -0.560569774 -0.655946292 low
## 448 0.34882541 0.530304459 -1.079992814 high
## 210 0.44061589 1.461538560 -0.275391721 med_high
## 387 0.44061589 2.188321265 -1.308325557 high
## 454 0.21026340 0.572315020 -0.514597451 high
## 389 0.17795052 2.516003640 -1.340944520 high
## 94 0.43437239 -0.902255670 0.268257666 low
## 431 -2.99276453 0.698346703 -0.873406047 high
## 25 0.41246535 0.510699530 -0.753803182 med_high
## 182 0.44061589 -0.448541612 1.486032293 low
## 91 0.38891529 -0.538164142 0.007305960 low
## 175 0.40041648 -0.421934923 0.007305960 med_low
## 203 0.42396655 -1.336364800 2.149284545 low
## 252 0.22340762 -1.269147903 0.246511690 med_low
## 402 0.44061589 1.073641047 -1.667134152 high
## 107 0.42714307 0.841182610 -0.329756660 med_low
## 336 0.44061589 -0.650192305 -0.155788856 low
## 139 0.38738179 1.213676250 -1.003881900 med_low
## 498 0.44061589 0.202622083 -0.460232513 med_high
## 356 0.21212550 -0.991878200 -0.210153795 med_low
## 266 0.39132506 -0.308506409 0.029051936 med_high
## 239 0.24903885 -0.881250390 0.126908825 med_low
## 495 0.44061589 0.131204129 0.213892727 med_high
## 259 0.29153851 -0.681000049 1.464286318 med_high
## 380 0.40600278 1.278092444 -1.340944520 high
## 134 0.35068751 0.332854822 -0.449359525 med_high
## 493 0.44061589 0.097595681 -0.264518733 med_low
## 221 0.38365760 -0.412132459 0.453098458 med_high
## 500 0.42823842 0.342657286 -0.547216415 med_low
## 416 -3.60835228 2.296148371 -1.667134152 high
## 497 0.44061589 1.188469914 -0.308010684 med_high
## 401 0.44061589 1.976868108 -1.841101956 high
## 350 0.36339359 -0.947066935 0.442225470 low
## 292 0.44061589 -1.273348959 1.605635158 low
## 443 0.42736214 0.551309739 -0.449359525 high
## 301 0.37445664 -0.921860599 0.246511690 low
## 373 -0.09632559 -0.528361678 2.986504601 high
## 200 0.44061589 -1.133313756 1.344683452 low
## 58 0.39680182 -1.218735230 0.985874857 low
## 101 0.41717537 -0.452742668 0.540082359 med_low
## 479 0.25221537 0.752960432 -0.862533059 high
## 439 -3.15159055 2.992123331 -1.536658299 high
## 323 0.44061589 -0.693603218 -0.231899770 med_high
## 208 0.35879311 0.757161488 -0.003567028 med_low
## 378 0.44061589 1.202473434 -1.003881900 high
## 125 0.24871025 0.689944590 -0.405867574 med_low
## 447 -0.42350719 0.719351983 -0.829914096 high
## 204 0.39548740 -1.238340158 2.823409785 low
## 32 0.21968342 0.054184768 -0.873406047 med_high
## 275 0.44061589 -1.277550015 1.072858759 low
## 445 -1.27229535 1.559563202 -1.275706593 high
## 108 0.33973399 0.201221731 -0.231899770 med_low
## 462 0.38070015 0.279641445 -0.525470439 high
## 230 0.25922563 -1.245341918 0.975001869 med_high
## 360 0.37314222 0.002371742 0.007305960 high
## 446 -3.43517715 1.586169891 -1.166976716 high
## 74 0.22450297 -0.716008850 0.094289862 med_low
## 64 0.42615725 -0.441539852 0.268257666 med_low
## 183 0.41016511 -1.096904603 1.670873085 med_low
## 250 0.40600278 -0.853243349 0.398733519 med_low
## 381 0.44061589 0.638131565 -1.319198544 high
## 362 -0.06598434 0.215225251 -0.286264709 high
## 205 0.37106105 -1.368572897 2.986504601 low
## 136 0.41618955 0.603122764 -0.481978488 med_high
## 417 -3.67056826 1.839633609 -1.634515189 high
## 119 -0.19764564 0.380466791 -0.231899770 med_low
## 54 0.44061589 -0.591377519 0.094289862 low
## 368 -2.46732424 0.094794977 0.061670899 high
## 166 -1.27623862 -0.398128939 0.268257666 med_high
## 289 0.44061589 -0.707606738 -0.025313003 low
## 341 0.44061589 -0.470947244 -0.416740562 low
## 351 0.44061589 -0.934463767 0.039924923 low
## 397 0.44061589 0.940607604 -1.090865802 high
## 244 0.19755732 -1.045091578 0.126908825 med_low
## 321 0.44061589 -0.763620819 0.137781813 med_low
## 41 0.42659539 -1.494604580 1.344683452 low
## 177 0.40041648 -0.356118378 0.072543887 low
## 287 -0.16511369 0.038780895 -0.264518733 low
## 98 0.44061589 -1.182326077 1.757856987 med_low
## 277 0.35682148 -0.924661303 1.159842661 med_low
## 145 0.44061589 2.329756820 -1.166976716 med_high
## 11 0.39263948 1.091845624 -0.819041108 med_low
## 285 0.41673722 -0.672597937 1.051112783 low
## 428 -3.70069044 0.261436868 -1.264833606 high
## 348 0.39165367 -0.881250390 0.061670899 low
## 17 0.33053303 -0.850442645 0.061670899 med_high
## 153 -0.14671178 -0.074647619 -0.786422145 med_high
## 31 0.03829315 1.392921311 -1.069119826 med_high
## 78 0.33173792 -0.333712745 -0.188407819 med_low
## 396 0.38672458 0.625528397 -1.025627875 high
## 248 0.21322085 -0.350516970 -0.221026782 med_low
## 120 0.38146689 0.134004834 -0.351502635 med_low
## 332 0.40906976 -0.031236706 -0.590708366 low
## 167 0.13829878 -1.253744030 2.986504601 med_high
## 357 0.23063694 0.692745294 -0.514597451 high
## 322 0.44061589 -0.809832436 0.061670899 med_low
## 46 0.44061589 -0.342114857 -0.351502635 med_low
## 419 -3.72665028 1.115651608 -1.493166348 high
## 131 0.42024235 -0.007430722 -0.362375623 med_high
## 75 0.41892793 -0.822435605 0.170400776 low
## 65 0.40052602 -0.644590896 1.138096685 low
## 283 0.22340762 -1.350368321 2.551585092 low
## 151 0.17663610 0.202622083 -0.112296905 med_high
## 95 0.44061589 -0.288901480 -0.210153795 low
## 319 0.42210445 -0.321109577 0.061670899 med_high
## 365 -0.02326562 -1.031088057 -0.068804954 med_high
## 104 0.41399884 0.110198849 -0.351502635 med_low
## 264 0.40249765 -0.196478246 0.920636930 med_high
## 444 0.32921861 0.867789298 -0.775549157 high
## 337 0.44061589 -0.399529291 -0.329756660 low
## 421 -0.41540159 0.331454470 -0.634200317 high
## 372 0.10379520 -0.437338796 2.986504601 high
## 106 0.40939837 0.534505515 -0.329756660 med_low
## 176 0.37555199 -1.025486649 0.746669127 low
## 189 0.28660942 -1.133313756 0.790161078 med_low
## 238 0.36580336 -1.109507771 0.975001869 med_high
## 100 0.44061589 -0.905056374 1.159842661 low
## 391 0.41356070 0.624128045 -0.808168120 high
## 195 0.21935482 -1.158520092 0.714050163 low
## 328 0.44061589 0.019175967 -0.036185991 med_low
## 354 0.30435412 -1.141715868 0.822780041 low
## 92 0.40392161 -0.623585616 -0.057931966 low
## 126 0.31048809 0.302047077 -0.123169893 med_low
## 45 0.35835497 -0.434538092 -0.144915868 med_low
## 307 0.44061589 -0.865846518 1.181588636 low
## 229 0.22822717 -1.222936286 2.627696006 med_high
## 290 0.16480630 -0.440139500 0.246511690 low
## 379 0.44061589 1.545559682 -1.025627875 high
## 455 -3.83366615 0.848184370 -0.829914096 high
## 172 -0.09358721 -0.087250788 -0.373248611 med_high
## 465 0.44061589 0.079391104 -0.123169893 high
## 261 0.39570647 -0.428936683 1.225080587 med_high
## 14 0.44061589 -0.615183504 -0.231899770 med_high
## 371 0.38749133 -1.357370081 2.986504601 high
## 201 0.30260156 -1.148717628 1.127223698 low
## 73 0.37500432 -0.998879961 0.029051936 med_low
## 181 0.42593818 -0.713208146 1.877459852 low
## 317 0.37270408 0.794970993 -0.514597451 med_high
## 164 0.34805866 -1.306957408 2.986504601 med_high
## 286 0.41673722 -0.619384560 -0.057931966 low
## 310 0.43338657 -0.375723306 -0.242772758 med_high
## 33 -1.35904722 2.108501199 -1.014754888 med_high
## 369 0.20642967 -1.315359520 2.986504601 high
## 128 0.38814854 0.635330861 -0.688565255 med_high
## 209 0.26996007 0.281041797 0.203019739 med_low
## 399 0.44061589 2.511802584 -1.906339882 high
## 309 0.44061589 -1.136114460 0.029051936 med_high
## 427 -3.63683142 0.425278056 -1.340944520 high
## 63 0.44061589 -0.829437365 -0.036185991 med_low
## 338 0.41772304 -0.293102536 -0.438486537 low
## 480 0.29186711 0.063987232 -0.123169893 high
## 467 -3.66574871 0.629729453 -0.384121599 high
## 199 0.38913436 -0.844841237 1.312064489 low
## 276 0.44061589 -1.354569377 1.029366808 med_low
## 473 0.40194997 0.239031236 0.072543887 med_high
## 324 0.37741409 -0.127860997 -0.438486537 med_high
## 115 0.35123518 -0.308506409 -0.438486537 med_low
## 171 -0.70523169 0.248833700 -0.558089402 med_high
## 48 0.39504926 0.860787538 -0.645073304 med_low
## 429 -2.84730180 1.241683291 -1.253960618 high
## 359 0.42451422 -0.164270149 0.018178948 high
## 89 0.44061589 -1.001680665 0.116035838 low
## 469 0.13216481 0.766963952 -0.373248611 high
## 299 0.12668805 -1.075899322 -0.003567028 low
## 96 0.01430495 -0.840640181 0.637939249 med_low
## 314 0.40216904 -0.665596177 -0.101423917 med_high
## 102 0.42615725 -0.697804274 0.431352482 med_low
## 110 0.37850944 0.405673128 -0.340629648 med_high
## 297 0.39625414 -0.737014131 0.496590409 low
## 406 0.30994042 1.446134688 -1.906339882 high
## 433 -2.83393851 -0.087250788 -0.699438243 high
## 302 0.42801935 -0.441539852 -0.057931966 low
## 142 0.44061589 3.046737061 -0.884279035 med_high
## 430 -3.24173801 1.600173411 -1.417055434 high
## 59 0.37248501 -0.811232788 0.083416874 med_low
## 184 0.44061589 -0.976474328 1.083731747 med_low
## 66 0.44061589 -1.117909883 0.105162850 low
## 156 -2.94281648 0.331454470 -0.753803182 med_high
## 452 -0.01516002 0.710949871 -0.797295133 high
## 494 0.44061589 -0.090051492 -0.079677942 med_low
## 240 0.29690573 -0.739814835 0.083416874 med_low
## 288 0.44061589 -0.772022931 0.072543887 low
## 334 0.36186010 -0.976474328 -0.036185991 low
## 235 0.03862176 -0.644590896 0.703177176 med_high
## 327 0.44061589 -0.910657783 0.050797911 med_high
## 7 0.42637632 -0.031236706 0.039924923 med_low
## 212 0.42243305 1.586169891 -0.351502635 med_high
## 502 0.38683412 -0.417733867 -0.014440015 low
## 335 0.35846451 -0.826636661 -0.199280807 low
## 342 0.41695629 -1.003081017 1.105477722 low
## 409 -0.46042055 1.925055083 -0.579835378 high
## 407 0.14837602 1.496547361 -1.156103728 high
## 300 0.16327280 -1.108107419 0.703177176 low
## 506 0.44061589 -0.668396881 -1.156103728 low
## 442 0.32078440 0.961612885 -0.590708366 high
## 13 0.37051338 0.428078760 -0.090550930 med_low
## 10 0.32899954 0.622727693 -0.394994586 med_low
## 53 0.44061589 -1.032488409 0.268257666 low
## 215 -0.08482439 2.366165973 0.126908825 med_high
## 404 0.44061589 0.996621685 -1.547531287 high
## 133 0.31859370 -0.214682823 0.050797911 med_high
## 311 -0.06817505 -0.001829314 -0.699438243 med_high
## 258 0.36175056 -1.054894042 2.986504601 med_high
## 273 0.41936607 -0.689402161 0.203019739 med_low
## 375 0.44061589 3.545262384 -0.949516961 high
## 487 0.39439205 0.325853062 -0.373248611 high
## 180 0.44061589 -1.066096858 1.594762170 low
## 87 0.43064819 0.028978431 -0.003567028 low
## 202 0.40633138 -0.731412722 0.170400776 low
## 186 0.33338095 0.069588640 0.768415102 low
## 304 0.36974663 -1.091303195 1.148969673 med_low
## 316 0.43535821 -0.161469445 -0.688565255 med_low
## 260 0.38617691 -0.805631380 0.822780041 med_high
## 47 0.44061589 0.209623843 -0.275391721 med_low
## 161 -0.19446912 -1.001680665 0.485717421 med_high
## 339 0.43229122 -0.580174703 -0.210153795 low
## 413 -3.59148386 3.041135653 -0.503724464 high
## 155 -0.39053710 0.345457990 -0.601581353 med_high
## 457 -3.79204278 0.890194931 -1.069119826 high
## 168 -1.41370528 -0.071846915 0.137781813 med_high
## 331 0.13030271 -0.498954285 -0.297137697 low
## 113 0.41925653 0.498096362 -0.405867574 med_low
## 474 0.19722871 -0.139063813 0.790161078 high
## 377 0.06951068 1.482543841 -0.938643973 high
## 247 0.36700825 -0.489151821 0.192146752 med_high
## 466 -0.24397902 0.206823139 -0.286264709 med_high
## 141 0.34400586 1.611376228 -0.927770986 med_high
## 325 0.44061589 -0.914858839 0.268257666 med_high
## 169 -0.65265480 -0.217483527 0.137781813 med_high
## 246 0.35550706 0.813175569 -0.438486537 med_low
## 256 0.42177584 -0.476548653 -0.177534831 low
## 282 0.38946296 -1.129112700 1.399048391 low
## 499 0.44061589 0.037380543 -0.144915868 med_low
## 67 0.44061589 -0.337913801 -0.340629648 low
## 265 0.34192469 -0.637589136 1.518651256 med_high
## 471 0.44061589 0.509299178 -0.286264709 high
## 451 -3.90333053 0.670339662 -0.993008912 high
## 370 0.20434850 -1.249542974 2.986504601 high## zn indus chas nox rm age
## 1 0.28454827 -1.28663623 -0.2723291 -0.14407485 0.41326292 -0.11989477
## 2 -0.48724019 -0.59279438 -0.2723291 -0.73953036 0.19408239 0.36680343
## 3 -0.48724019 -0.59279438 -0.2723291 -0.73953036 1.28144555 -0.26554897
## 6 -0.48724019 -1.30558569 -0.2723291 -0.83445805 0.20689164 -0.35080997
## 8 0.04872402 -0.47618230 -0.2723291 -0.26489191 -0.16030692 0.97784057
## 12 0.04872402 -0.47618230 -0.2723291 -0.26489191 -0.39229670 0.50890509
## 15 -0.48724019 -0.43682573 -0.2723291 -0.14407485 -0.26847393 0.56574575
## 16 -0.48724019 -0.43682573 -0.2723291 -0.14407485 -0.64136549 -0.42896588
## 21 -0.48724019 -0.43682573 -0.2723291 -0.14407485 -1.01710355 1.04889141
## 24 -0.48724019 -0.43682573 -0.2723291 -0.14407485 -0.67125374 1.11638970
## 26 -0.48724019 -0.43682573 -0.2723291 -0.14407485 -0.97582929 0.60837625
## 27 -0.48724019 -0.43682573 -0.2723291 -0.14407485 -0.67125374 0.77179316
## 29 -0.48724019 -0.43682573 -0.2723291 -0.14407485 0.29940290 0.91744737
## 36 -0.48724019 -0.75459363 -0.2723291 -0.48063666 -0.50046372 -0.01331852
## 49 -0.48724019 -0.61611679 -0.2723291 -0.92075595 -1.26047933 0.94942024
## 57 3.15731641 -1.51548743 -0.2723291 -1.24868797 0.13999888 -1.16789453
## 70 0.04872402 -0.73855947 -0.2723291 -1.25731776 -0.56877973 -1.26381315
## 90 -0.48724019 -1.12629463 -0.2723291 -0.56693456 1.13058103 -0.19449814
## 103 -0.48724019 -0.37560439 -0.2723291 -0.29941107 0.17131038 0.59771863
## 105 -0.48724019 -0.37560439 -0.2723291 -0.29941107 -0.16742317 0.76113554
## 109 -0.48724019 -0.37560439 -0.2723291 -0.29941107 0.26951465 1.01336599
## 112 -0.48724019 -0.16424500 -0.2723291 -0.06640675 0.61251795 0.46272205
## 114 -0.48724019 -0.16424500 -0.2723291 -0.06640675 -0.27416693 0.95297278
## 121 -0.48724019 2.11552109 -0.2723291 0.22700611 -0.59012848 0.03996960
## 127 -0.48724019 2.11552109 -0.2723291 0.22700611 -0.95590379 0.96007787
## 129 -0.48724019 1.56744433 -0.2723291 0.59808708 0.20831489 1.07375920
## 143 -0.48724019 1.23072696 3.6647712 2.72964520 -1.25478633 1.11638970
## 144 -0.48724019 1.23072696 -0.2723291 2.72964520 -1.16227507 1.11638970
## 146 -0.48724019 1.23072696 -0.2723291 2.72964520 -0.22008342 1.11638970
## 149 -0.48724019 1.23072696 -0.2723291 2.72964520 -1.56363163 0.89613212
## 150 -0.48724019 1.23072696 -0.2723291 2.72964520 -0.97867579 0.93521008
## 152 -0.48724019 1.23072696 -0.2723291 2.72964520 -1.25336308 1.11638970
## 157 -0.48724019 1.23072696 -0.2723291 2.72964520 -1.44123211 0.90323720
## 158 -0.48724019 1.23072696 -0.2723291 0.43412107 0.93701900 1.02402361
## 159 -0.48724019 1.23072696 -0.2723291 0.43412107 -0.31117144 1.11638970
## 165 -0.48724019 1.23072696 -0.2723291 0.43412107 -0.61290048 0.82508129
## 170 -0.48724019 1.23072696 -0.2723291 0.43412107 0.16704063 0.94586770
## 179 -0.48724019 -1.03300497 -0.2723291 -0.38570897 0.81888923 0.20693906
## 185 -0.48724019 -1.26477147 -0.2723291 -0.57556435 -0.96871304 0.75403046
## 190 1.44223095 -1.12192167 -0.2723291 -1.01568364 1.28144555 -1.05421320
## 191 1.44223095 -1.12192167 -0.2723291 -1.01568364 0.94840500 -1.67235543
## 198 2.94293073 -1.40179066 -0.2723291 -1.30046671 1.17043203 -1.13592165
## 206 -0.48724019 -0.07970124 -0.2723291 -0.56693456 -0.56024023 -1.64393510
## 213 -0.48724019 -0.07970124 3.6647712 -0.56693456 -0.67979324 -0.52488450
## 216 -0.48724019 -0.07970124 -0.2723291 -0.56693456 -0.14607441 -0.92987424
## 217 -0.48724019 0.40132357 3.6647712 -0.04051738 -0.56450998 -0.44672859
## 223 -0.48724019 -0.71961001 3.6647712 -0.41159834 0.84593099 0.32417293
## 224 -0.48724019 -0.71961001 -0.2723291 -0.41159834 0.47446268 0.43430172
## 225 -0.48724019 -0.71961001 -0.2723291 -0.43748771 2.81997903 0.34548818
## 226 -0.48724019 -0.71961001 -0.2723291 -0.43748771 3.47325088 0.51245763
## 227 -0.48724019 -0.71961001 -0.2723291 -0.43748771 2.49832448 0.63679658
## 233 -0.48724019 -0.71961001 -0.2723291 -0.41159834 2.92102980 0.16786110
## 237 -0.48724019 -0.71961001 3.6647712 -0.41159834 0.49296493 0.28154243
## 243 0.79907391 -0.90473168 -0.2723291 -1.09335175 0.10441762 -0.55685738
## 245 0.45605682 -0.76917014 -0.2723291 -1.06746238 -0.98436879 0.28154243
## 251 0.45605682 -0.76917014 -0.2723291 -1.06746238 0.28801690 -1.97432146
## 257 3.37170210 -1.07673449 -0.2723291 -1.38676461 1.66429986 -1.22118265
## 263 0.37030254 -1.04466617 -0.2723291 0.79657225 3.00784806 0.81442366
## 274 0.37030254 -0.60882854 3.6647712 -0.78267931 2.00161016 -0.59593534
## 279 1.22784527 -0.68899934 -0.2723291 -0.92938574 0.28090065 -1.29578602
## 280 0.37030254 -1.13795583 -0.2723291 -0.96476788 0.75057322 -1.29223348
## 294 -0.48724019 0.40569652 -0.2723291 -1.01568364 -0.22435318 -1.78248422
## 295 -0.48724019 0.40569652 -0.2723291 -1.01568364 -0.39229670 -0.93342678
## 298 -0.48724019 0.40569652 -0.2723291 -1.01568364 -0.70398850 -0.37567776
## 308 0.92770532 -1.30558569 -0.2723291 -0.71364099 0.80323348 0.06128485
## 320 -0.48724019 -0.18027916 -0.2723291 -0.09229612 -0.24427868 -0.34725743
## 347 -0.48724019 -0.98344483 -0.2723291 -0.97253469 -0.55027747 -0.57817263
## 355 2.94293073 -1.34494227 -0.2723291 -1.22279860 -0.88474128 -1.65814526
## 358 -0.48724019 1.01499462 3.6647712 1.85803641 0.15707788 0.79666096
## 364 -0.48724019 1.01499462 3.6647712 1.85803641 -0.68548625 0.72561012
## 366 -0.48724019 1.01499462 -0.2723291 1.40928733 -3.87641323 0.68653217
## 367 -0.48724019 1.01499462 -0.2723291 1.40928733 -1.88101643 0.81087112
## 374 -0.48724019 1.01499462 -0.2723291 0.97779784 -1.96214169 1.11638970
## 376 -0.48724019 1.01499462 -0.2723291 1.00368721 1.46362158 1.04178632
## 382 -0.48724019 1.01499462 -0.2723291 1.00368721 0.37056541 1.08441682
## 385 -0.48724019 1.01499462 -0.2723291 1.25395112 -2.72785030 0.80376604
## 386 -0.48724019 1.01499462 -0.2723291 1.25395112 -1.43411586 1.04889141
## 390 -0.48724019 1.01499462 -0.2723291 1.25395112 -1.27328858 1.07731174
## 393 -0.48724019 1.01499462 -0.2723291 1.25395112 -1.77711916 1.00981345
## 394 -0.48724019 1.01499462 -0.2723291 1.19354259 -0.13041866 0.85350162
## 403 -0.48724019 1.01499462 -0.2723291 1.19354259 0.16988713 1.11638970
## 408 -0.48724019 1.01499462 -0.2723291 0.90012973 -0.96302004 1.11638970
## 414 -0.48724019 1.01499462 -0.2723291 0.36508275 -1.60775238 1.11638970
## 422 -0.48724019 1.01499462 -0.2723291 1.40928733 -0.39656645 0.94942024
## 441 -0.48724019 1.01499462 -0.2723291 1.59914271 -0.66413749 0.84639654
## 449 -0.48724019 1.01499462 -0.2723291 1.36613839 -0.14180466 1.07020666
## 450 -0.48724019 1.01499462 -0.2723291 1.36613839 0.18838939 1.05599649
## 458 -0.48724019 1.01499462 -0.2723291 1.36613839 -0.49619397 0.41653901
## 459 -0.48724019 1.01499462 -0.2723291 1.36613839 0.02329236 0.53732542
## 460 -0.48724019 1.01499462 -0.2723291 1.36613839 -0.28982269 0.56219321
## 461 -0.48724019 1.01499462 -0.2723291 1.36613839 0.59259245 0.76113554
## 463 -0.48724019 1.01499462 -0.2723291 1.36613839 0.04606437 0.51245763
## 468 -0.48724019 1.01499462 -0.2723291 0.25289548 -0.40083620 0.92099991
## 470 -0.48724019 1.01499462 -0.2723291 0.21837632 -0.81357876 -0.42186080
## 475 -0.48724019 1.01499462 -0.2723291 0.25289548 -1.22062833 0.95297278
## 476 -0.48724019 1.01499462 -0.2723291 0.25289548 -0.17453942 1.02402361
## 478 -0.48724019 1.01499462 -0.2723291 0.51178918 -1.39568810 1.02047107
## 483 -0.48724019 1.01499462 -0.2723291 -0.19585359 1.10496252 0.29930514
## 489 -0.48724019 2.42017014 -0.2723291 0.46864023 -1.18220057 0.85705416
## 490 -0.48724019 2.42017014 -0.2723291 0.46864023 -1.23913058 1.05599649
## 503 -0.48724019 0.11562398 -0.2723291 0.15796779 -0.23431593 0.28864751
## 505 -0.48724019 0.11562398 -0.2723291 0.15796779 0.72495472 0.73626775
## dis rad tax ptratio black
## 1 0.140074984 -0.9818712 -0.66594918 -1.45755797 0.440615895
## 2 0.556609050 -0.8670245 -0.98635338 -0.30279450 0.440615895
## 3 0.556609050 -0.8670245 -0.98635338 -0.30279450 0.396035074
## 6 1.076671135 -0.7521778 -1.10502160 0.11292035 0.410165113
## 8 1.023624897 -0.5224844 -0.57694801 -1.50374851 0.440615895
## 12 1.154792049 -0.5224844 -0.57694801 -1.50374851 0.440615895
## 15 0.316689987 -0.6373311 -0.60068166 1.17530274 0.255720500
## 16 0.334118787 -0.6373311 -0.60068166 1.17530274 0.426595391
## 21 0.001356935 -0.6373311 -0.60068166 1.17530274 0.217930861
## 24 0.142544460 -0.6373311 -0.60068166 1.17530274 0.414765591
## 26 0.313223223 -0.6373311 -0.60068166 1.17530274 -0.583319029
## 27 0.421215295 -0.6373311 -0.60068166 1.17530274 0.221326452
## 29 0.313270713 -0.6373311 -0.60068166 1.17530274 0.342472368
## 36 -0.206458943 -0.5224844 -0.76681717 0.34387304 0.440615895
## 49 0.985395514 -0.7521778 -1.03975408 -0.25660396 0.440615895
## 57 2.560921014 -0.8670245 -0.56508119 -0.53374719 0.440615895
## 70 1.283632195 -0.6373311 -0.37521203 0.20530143 0.440615895
## 90 -0.180719408 -0.8670245 -0.82021787 -0.30279450 0.431414939
## 103 -0.513053850 -0.5224844 -0.14380900 1.12911220 -3.131326538
## 105 -0.652531738 -0.5224844 -0.14380900 1.12911220 0.394501581
## 109 -0.646880437 -0.5224844 -0.14380900 1.12911220 0.422433054
## 112 -0.530720099 -0.4076377 0.14099473 -0.30279450 0.426266786
## 114 -0.592219542 -0.4076377 0.14099473 -0.30279450 0.440615895
## 121 -0.730082773 -0.8670245 -1.30675758 0.29768250 0.355726125
## 127 -0.967769809 -0.8670245 -1.30675758 0.29768250 0.028654058
## 129 -0.941507885 -0.6373311 0.17066179 1.26768382 0.440615895
## 143 -1.174635890 -0.5224844 -0.03107419 -1.73470120 0.440615895
## 144 -1.131799984 -0.5224844 -0.03107419 -1.73470120 0.440615895
## 146 -1.128333220 -0.5224844 -0.03107419 -1.73470120 -2.012862748
## 149 -1.075856861 -0.5224844 -0.03107419 -1.73470120 0.003460966
## 150 -1.077708968 -0.5224844 -0.03107419 -1.73470120 -0.052840120
## 152 -1.046413113 -0.5224844 -0.03107419 -1.73470120 -0.165113687
## 157 -0.977647712 -0.5224844 -0.03107419 -1.73470120 -2.936025300
## 158 -0.910734419 -0.5224844 -0.03107419 -1.73470120 0.074001626
## 159 -0.967722319 -0.5224844 -0.03107419 -1.73470120 -0.030494942
## 165 -0.652056838 -0.5224844 -0.03107419 -1.73470120 0.421009097
## 170 -0.727803257 -0.5224844 -0.03107419 -1.73470120 -0.291736362
## 179 -0.417789076 -0.5224844 -0.66594918 -0.85708096 0.378947585
## 185 -0.383311396 -0.7521778 -1.27709053 -0.30279450 0.375990135
## 190 0.366459420 -0.5224844 -0.06074124 -1.50374851 0.440615895
## 191 1.274989030 -0.5224844 -0.06074124 -1.50374851 0.230089266
## 198 1.668775425 -0.8670245 -0.47014661 -2.70470251 -0.025894464
## 206 0.071404563 -0.6373311 -0.77868399 0.06672981 0.440615895
## 213 -0.067645915 -0.6373311 -0.77868399 0.06672981 0.375332924
## 216 0.071404563 -0.6373311 -0.77868399 0.06672981 0.404797889
## 217 -0.324328918 -0.5224844 -0.78461740 -0.94946204 0.395706469
## 223 -0.248345051 -0.1779443 -0.60068166 -0.48755665 0.369308489
## 224 -0.248345051 -0.1779443 -0.60068166 -0.48755665 0.440615895
## 225 -0.427714469 -0.1779443 -0.60068166 -0.48755665 0.310816699
## 226 -0.427714469 -0.1779443 -0.60068166 -0.48755665 0.277408467
## 227 -0.275129364 -0.1779443 -0.60068166 -0.48755665 0.336338397
## 233 0.020590352 -0.1779443 -0.60068166 -0.48755665 0.320236725
## 237 0.167619136 -0.1779443 -0.60068166 -0.48755665 0.348058662
## 243 1.538890501 -0.4076377 -0.64221553 -0.85708096 0.176088420
## 245 1.975512802 -0.2927910 -0.46421320 0.29768250 0.173240505
## 251 1.710424083 -0.2927910 -0.46421320 0.29768250 0.433824713
## 257 1.206746019 -0.7521778 -0.97448656 -1.18041474 0.324946738
## 263 -0.715455878 -0.5224844 -0.85581834 -2.51994036 0.330642568
## 274 0.271384606 -0.7521778 -1.09908819 0.06672981 0.373470826
## 279 0.163962412 -0.6373311 -0.91515245 -0.39517558 0.440615895
## 280 0.145156405 -0.5224844 -1.14062207 -1.64232012 0.440615895
## 294 0.810965047 -0.6373311 -0.70748306 -1.13422420 0.440615895
## 295 0.810965047 -0.6373311 -0.70748306 -1.13422420 0.440615895
## 298 1.199100142 -0.6373311 -0.70748306 -1.13422420 0.440615895
## 308 -0.290801037 -0.2927910 -1.10502160 -0.02565127 0.440615895
## 320 0.098236367 -0.6373311 -0.61848189 -0.02565127 0.433277038
## 347 2.003389383 -0.7521778 -0.33367816 0.15911089 0.086926778
## 355 3.224877549 -0.6373311 -0.44047956 1.63720813 0.286171282
## 358 -0.612545227 1.6596029 1.52941294 0.80577843 0.379714331
## 364 -0.897722181 1.6596029 1.52941294 0.80577843 -0.039805433
## 366 -1.036155290 1.6596029 1.52941294 0.80577843 -0.021622592
## 367 -0.970096815 1.6596029 1.52941294 0.80577843 -0.445195159
## 374 -1.244636028 1.6596029 1.52941294 0.80577843 0.440615895
## 376 -1.177152855 1.6596029 1.52941294 0.80577843 0.440615895
## 382 -1.080795813 1.6596029 1.52941294 0.80577843 0.440615895
## 385 -1.118645277 1.6596029 1.52941294 0.80577843 -0.775991422
## 386 -1.125008926 1.6596029 1.52941294 0.80577843 0.440615895
## 390 -0.981589375 1.6596029 1.52941294 0.80577843 0.440615895
## 393 -0.961691100 1.6596029 1.52941294 0.80577843 0.440615895
## 394 -0.951623237 1.6596029 1.52941294 0.80577843 0.440615895
## 403 -1.023902892 1.6596029 1.52941294 0.80577843 0.212892242
## 408 -1.191922219 1.6596029 1.52941294 0.80577843 -0.269281649
## 414 -1.047457891 1.6596029 1.52941294 0.80577843 -1.595971828
## 422 -0.912016646 1.6596029 1.52941294 0.80577843 -0.401928760
## 441 -0.916005799 1.6596029 1.52941294 0.80577843 0.380919218
## 449 -0.728230666 1.6596029 1.52941294 0.80577843 0.440615895
## 450 -0.764607943 1.6596029 1.52941294 0.80577843 -0.574665749
## 458 -0.482422853 1.6596029 1.52941294 0.80577843 -3.868498343
## 459 -0.480570747 1.6596029 1.52941294 0.80577843 -0.925178346
## 460 -0.511724132 1.6596029 1.52941294 0.80577843 0.440615895
## 461 -0.568712033 1.6596029 1.52941294 0.80577843 -1.111169093
## 463 -0.503698336 1.6596029 1.52941294 0.80577843 0.440615895
## 468 -0.595876266 1.6596029 1.52941294 0.80577843 -0.278044464
## 470 -0.461289840 1.6596029 1.52941294 0.80577843 0.440615895
## 475 -0.648352625 1.6596029 1.52941294 0.80577843 -0.044844052
## 476 -0.754635060 1.6596029 1.52941294 0.80577843 -0.590548351
## 478 -0.804641943 1.6596029 1.52941294 0.80577843 -0.078799960
## 483 -0.182571515 1.6596029 1.52941294 0.80577843 0.422871195
## 489 -0.937518732 -0.6373311 1.79641644 0.75958789 0.420790026
## 490 -0.968624628 -0.6373311 1.79641644 0.75958789 -0.138277566
## 503 -0.715930777 -0.9818712 -0.80241764 1.17530274 0.440615895
## 505 -0.667776001 -0.9818712 -0.80241764 1.17530274 0.402826256
## lstat medv crime
## 1 -1.074498970 0.15952779 low
## 2 -0.491952525 -0.10142392 low
## 3 -1.207532413 1.32293748 low
## 6 -1.042290874 0.67055821 low
## 8 0.909799859 0.49659041 med_low
## 12 0.086392864 -0.39499459 med_low
## 15 -0.335113097 -0.47110550 med_high
## 16 -0.585776111 -0.28626471 med_high
## 21 1.171665689 -0.97126294 med_high
## 24 1.012025558 -0.87340605 med_high
## 26 0.540106923 -0.93864397 med_high
## 27 0.302047077 -0.64507330 med_high
## 29 0.020576319 -0.44935953 med_high
## 36 -0.416333515 -0.39499459 low
## 49 2.542610329 -0.88427903 med_low
## 57 -0.963871160 0.23563870 low
## 70 -0.540964846 -0.17753483 med_low
## 90 -0.973673624 0.67055821 low
## 103 -0.283300072 -0.42761355 med_low
## 105 -0.045240227 -0.26451873 med_low
## 109 -0.053642339 -0.29713770 med_low
## 112 -0.349116618 0.02905194 med_low
## 114 0.621327341 -0.41674056 med_low
## 121 0.240431588 -0.05793197 low
## 127 2.045485358 -0.74293019 med_high
## 129 0.383267495 -0.49285148 med_high
## 143 1.983869868 -0.99300891 med_high
## 144 1.927855787 -0.75380318 high
## 146 2.121104367 -0.94951696 med_high
## 149 2.193922673 -0.51459745 med_high
## 150 1.231880827 -0.77554916 med_high
## 152 0.087793216 -0.31888367 med_high
## 157 0.488293898 -1.02562788 med_high
## 158 -1.129112700 2.04055467 med_high
## 159 -0.871447926 0.19214675 med_high
## 165 -0.141864517 0.01817895 med_high
## 170 -0.186675782 -0.02531300 med_high
## 179 -0.802830676 0.80103407 low
## 185 0.185817859 0.42047949 med_low
## 190 -1.017084537 1.34468345 med_low
## 191 -1.057694746 1.57301619 med_low
## 198 -0.566171183 0.84452602 low
## 206 -0.249691623 0.00730596 med_low
## 213 0.472890025 -0.01444002 med_low
## 216 -0.445740908 0.26825767 med_low
## 217 0.120001313 0.08341687 low
## 223 -0.381324714 0.54008236 med_high
## 224 -0.707606738 0.82278004 med_high
## 225 -1.192128541 2.42110924 med_high
## 226 -1.123511291 2.98650460 med_high
## 227 -1.333564096 1.63825412 med_high
## 233 -1.425987330 2.08404662 med_high
## 237 -0.435938444 0.27913065 med_high
## 243 -0.200679302 -0.03618599 med_low
## 245 -0.021434242 -0.53634343 med_low
## 251 -0.945666583 0.20301974 med_low
## 257 -1.336364800 2.33412534 low
## 263 -0.944266231 2.85602875 med_high
## 274 -0.850442645 1.37730242 med_low
## 279 -0.765021171 0.71405016 low
## 280 -1.092703547 1.36642943 med_low
## 294 -0.570372239 0.14865480 med_low
## 295 -0.315508169 -0.09055093 low
## 298 0.446283337 -0.24277276 med_low
## 308 -0.717409202 0.61619327 low
## 320 0.010773855 -0.16666184 med_high
## 347 0.002371742 -0.57983538 low
## 355 -0.644590896 -0.47110550 low
## 358 0.086392864 -0.09055093 high
## 364 0.278241093 -0.62332733 high
## 366 -0.774823635 0.54008236 high
## 367 0.188618563 -0.06880495 high
## 374 3.097149734 -0.94951696 high
## 376 0.110198849 -0.81904111 high
## 382 1.180067802 -1.26483361 high
## 385 2.517403992 -1.49316635 high
## 386 2.542610329 -1.66713415 high
## 390 1.147859705 -1.19959568 high
## 393 1.824229736 -1.39530946 high
## 394 0.352459751 -0.94951696 high
## 403 1.072240695 -1.13435775 high
## 408 -0.073247267 0.58357431 high
## 414 1.040032598 -0.67769227 high
## 422 0.426678408 -0.90602501 high
## 441 1.324304061 -1.30832556 high
## 449 0.766963952 -0.91689800 high
## 450 0.932205492 -1.03650086 high
## 458 0.600322060 -0.98213592 high
## 459 0.500897066 -0.82991410 high
## 460 0.286643205 -0.27539172 high
## 461 0.527503755 -0.66681928 high
## 463 0.187218211 -0.32975666 high
## 468 1.213676250 -0.37324861 high
## 470 0.295045317 -0.26451873 high
## 475 0.768364304 -0.94951696 high
## 476 1.602974115 -1.00388190 high
## 478 1.716402630 -1.14523074 high
## 483 -0.790227508 0.26825767 high
## 489 0.757161488 -0.79729513 med_low
## 490 1.584769539 -1.68888013 med_low
## 503 -0.500354637 -0.21015379 low
## 505 -0.864446166 -0.05793197 med_low4.5 Fit the linear discriminant analysis on the train set. Use the categorical crime rate (“crime”) as the target variable and all the other variables in the dataset as predictor variables. Draw the LDA (bi)plot.
## Call:
## lda(crime ~ ., data = train)
##
## Prior probabilities of groups:
## low med_low med_high high
## 0.2698020 0.2500000 0.2425743 0.2376238
##
## Group means:
## zn indus chas nox rm
## low 1.0360783 -0.9525935 -0.12784833 -0.9101627 0.47716555
## med_low -0.1026195 -0.3043382 -0.03844192 -0.5672763 -0.14372112
## med_high -0.3629840 0.1702413 0.20976484 0.3375203 0.07769538
## high -0.4872402 1.0149946 -0.06727176 1.0339814 -0.32128245
## age dis rad tax ptratio
## low -0.9543183 0.9208545 -0.6826376 -0.7279506 -0.45746924
## med_low -0.3859133 0.3602058 -0.5418150 -0.5071570 -0.02976726
## med_high 0.3282692 -0.3629358 -0.3912310 -0.2804591 -0.22643871
## high 0.8039141 -0.8591920 1.6596029 1.5294129 0.80577843
## black lstat medv
## low 0.3810478 -0.79265564 0.55275089
## med_low 0.3457725 -0.15570166 -0.01304052
## med_high 0.1082593 -0.01218906 0.16618472
## high -0.9939756 0.89668615 -0.68041051
##
## Coefficients of linear discriminants:
## LD1 LD2 LD3
## zn 0.10272977 0.729572657 -0.83061170
## indus -0.02218105 -0.352054987 0.43359857
## chas -0.06459343 -0.073375319 0.05199302
## nox 0.30888169 -0.715477057 -1.50495131
## rm -0.08673897 0.008977995 -0.16461288
## age 0.28801291 -0.181157713 -0.06933376
## dis -0.11680771 -0.231461583 0.17555279
## rad 3.08390782 0.975745080 0.44279663
## tax 0.08059777 -0.005138075 0.05719437
## ptratio 0.13362982 0.089543556 -0.28370428
## black -0.19799490 -0.037052465 0.16891607
## lstat 0.18594269 -0.233128273 0.28071101
## medv 0.17836518 -0.313724797 -0.30446991
##
## Proportion of trace:
## LD1 LD2 LD3
## 0.9471 0.0400 0.0129
- According to the linear description fit you can see how most of the high crime category correlates with the rad (index of accessibility to radial highways).
4.6 Save the crime categories from the test set and then remove the categorical crime variable from the test dataset. Then predict the classes with the LDA model on the test data. Cross tabulate the results with the crime categories from the test set.
## [1] low low low low med_low med_low med_high
## [8] med_high med_high med_high med_high med_high med_high low
## [15] med_low low med_low low med_low med_low med_low
## [22] med_low med_low low med_high med_high med_high high
## [29] med_high med_high med_high med_high med_high med_high med_high
## [36] med_high med_high low med_low med_low med_low low
## [43] med_low med_low med_low low med_high med_high med_high
## [50] med_high med_high med_high med_high med_low med_low med_low
## [57] low med_high med_low low med_low med_low low
## [64] med_low low med_high low low high high
## [71] high high high high high high high
## [78] high high high high high high high
## [85] high high high high high high high
## [92] high high high high high high high
## [99] med_low med_low low med_low
## Levels: low med_low med_high high## predicted
## correct low med_low med_high high
## low 8 10 0 0
## med_low 5 13 7 0
## med_high 0 8 20 0
## high 0 0 1 30- You can see how the predicted and corrected data tend to agree on the most extreme values (“low” and “high”), in the “med-low” and “med-high” you can see the most discrepance between the correct data and the predicted one.
4.7 Reload the Boston dataset and standardize the dataset (we did not do this in the Datacamp exercises, but you should scale the variables to get comparable distances). Calculate the distances between the observations.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.1343 3.4625 4.8241 4.9111 6.1863 14.3970## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.2662 8.4832 12.6090 13.5488 17.7568 48.8618- You can see how the two methods to calculate the distances between the variables , gives you as result different numbers, but you can also note how the trend between the variations is maintained.
4.7.1 Run k-means algorithm on the dataset. Investigate what is the optimal number of clusters and run the algorithm again. Visualize the clusters (for example with the pairs() or ggpairs() functions, where the clusters are separated with colors):
While checking for the optimal number of clusters you should look in the graph when defining the k max = 10 for the k value where the curve varies the most dramatically. That appears to be around k = 2
When exploring the pairs using the colors to separate the km clusters, you can see that the variable that better separetes the two clusters (Red Vs Black cluster) would be tax (full-value property-tax rate per $10,000) and rad (index of accessibility to radial highways). An almost complete cluster separation can also be observed when you check the crim (per capita crime rate by town) and black (1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town) variables.
4.8 Optional / Bonus sections:
4.8.1 Perform k-means on the original Boston data with some reasonable number of clusters (> 2). Remember to standardize the dataset.
For the reasonable amount of clusters (> 2) I select k = 3 as it was the following position in the curve you could observe a dramatically change.
Now when you check at the pairs with the clusters divided by colors, since we have more clusters it gets a bit more confusing to read the data. Nonetheless, after careful observation you the variables were you can more easily identify the different clusters (Red, Black and Green) are medv (median value of owner-occupied homes in $1000s) and partialy successful will be age (proportion of owner-occupied units built prior to 1940).
4.8.2 Then perform LDA using the clusters as target classes. Include all the variables in the Boston data in the LDA model. Visualize the results with a biplot (include arrows representing the relationships of the original variables to the LDA solution).
I was trying the following approach but I guess I missed something, further work/learning required in this section ; if the peer review knows how to fix this and explain me what is wrong I highly appreciate it!!
k-means clustering km <-kmeans(boston_scaled, centers = 3)
linear discriminant analysis lda.fit <- lda(km ~ . , data = boston_scaled$km)
print the lda.fit object lda.fit
function for the lda biplot arrows lda.arrows <- function(x, myscale = 2, arrow_heads = 0.1, color = “red”, tex = 0.75, choices = c(1,2)){ heads <- coef(x) arrows(x0 = 0, y0 = 0, x1 = myscale * heads[,choices[1]], y1 = myscale * heads[,choices[2]], col=color, length = arrow_heads) text(myscale * heads[,choices], labels = row.names(heads), cex = tex, col=color, pos=3) }
target classes as numeric classes <- as.numeric(boston_scaled$km)
plot the lda results plot(lda.fit, dimen = 2, col = classes, pch = classes) lda.arrows(lda.fit, myscale = 5)
I got stuck in this section as unfortunetely I couldn’t manage to fix the errors in my code
4.9 Super-Bonus: Run the provided code for the (scaled) train data that you used to fit the LDA. The code creates a matrix product, which is a projection of the data points.
## [1] 404 13## [1] 13 3##
## Attaching package: 'plotly'## The following object is masked from 'package:MASS':
##
## select## The following object is masked from 'package:ggplot2':
##
## last_plot## The following object is masked from 'package:stats':
##
## filter## The following object is masked from 'package:graphics':
##
## layout## Warning: 'scatter3d' objects don't have these attributes: 'col'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'x', 'y', 'z', 'text', 'hovertext', 'mode', 'surfaceaxis', 'surfacecolor', 'projection', 'connectgaps', 'line', 'marker', 'textposition', 'textfont', 'error_x', 'error_y', 'error_z', 'scene', 'xcalendar', 'ycalendar', 'zcalendar', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'xsrc', 'ysrc', 'zsrc', 'textsrc', 'hovertextsrc', 'textpositionsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'4.9.1 Draw another 3D plot where the color is defined by the clusters of the k-means. How do the plots differ?
- If I performed this correcly it seems that they don’t differ much. Maybe the clusters don’t separate that well the the data in the extreme negative x values (-2 < x < -4 ).